Functions Questions and Answers
![Analyze the polynomial function f(x)= x^3 + x^2 - 6x
(a) Determine the end behavior of the graph of the function.](https://media.kunduz.com/media/sug-question/raw/76902270-1658849271.6625783.jpeg?w=256)
Math
FunctionsAnalyze the polynomial function f(x)= x^3 + x^2 - 6x
(a) Determine the end behavior of the graph of the function.
![If f(x) = (x +1)/x-1, find the domain of f.
a)all real number greater than 1
b)all real numbers except 1 and -1
c)all real numbers less than -1
d)all real numbers
e) all real numbers except 1](https://media.kunduz.com/media/sug-question/raw/76948657-1658847989.2148106.jpeg?w=256)
Math
FunctionsIf f(x) = (x +1)/x-1, find the domain of f.
a)all real number greater than 1
b)all real numbers except 1 and -1
c)all real numbers less than -1
d)all real numbers
e) all real numbers except 1
![If f(x) = -4|3x - 2| and g(x) = -20, solve the following.
(a) f(x) = g(x)
(b) f(x) >g(x)
(c) f(x) = g(x)
(a) Solve f(x) = g(x). Select the correct choice below and, if necessary, fill in the answer box to complete your answer.
A. The solution set is {□ }.
(Simplify your answer. Use a comma to separate answers as needed.)
B. The solution set is {x| □} .
(Simplify your answer. Type a compound inequality.)
C. The solution set is {x|x≤□ or x≥□}.
(Simplify your answer. Type inequalities.)
D. The solution set is the empty set.](https://media.kunduz.com/media/sug-question/raw/77063442-1658847393.3125212.jpeg?w=256)
Math
FunctionsIf f(x) = -4|3x - 2| and g(x) = -20, solve the following.
(a) f(x) = g(x)
(b) f(x) >g(x)
(c) f(x) = g(x)
(a) Solve f(x) = g(x). Select the correct choice below and, if necessary, fill in the answer box to complete your answer.
A. The solution set is {□ }.
(Simplify your answer. Use a comma to separate answers as needed.)
B. The solution set is {x| □} .
(Simplify your answer. Type a compound inequality.)
C. The solution set is {x|x≤□ or x≥□}.
(Simplify your answer. Type inequalities.)
D. The solution set is the empty set.
![The function below gives the cost in dollars to manufacture x items:
C (x) = 10,000 + 5x-x^2/10,000
Find the average cost per item over the interval [1,000, 1,010].](https://media.kunduz.com/media/sug-question/raw/76848710-1658847224.8190172.jpeg?w=256)
Math
FunctionsThe function below gives the cost in dollars to manufacture x items:
C (x) = 10,000 + 5x-x^2/10,000
Find the average cost per item over the interval [1,000, 1,010].
![The plane area is bounded by the functions y=x^2 and y=4x - x^2 Find the volume generated when the plane area is revolved about the line y=6](https://media.kunduz.com/media/sug-question/raw/77109507-1658847155.927539.jpeg?w=256)
Math
FunctionsThe plane area is bounded by the functions y=x^2 and y=4x - x^2 Find the volume generated when the plane area is revolved about the line y=6
![Let f(x) =– 4x² +5/1 +x²
The graph of f is given below. Use the graph of f to determine the given limits. Enter DNE if a limit fails to exist, except in case of an infinite limit. If an infinite limit exists, enter ∞, or -∞, as appropriate.
lim f(x)=________
x->-∞
lim f(x)=________
x->∞](https://media.kunduz.com/media/sug-question/raw/77062423-1658845667.4268923.jpeg?w=256)
Math
FunctionsLet f(x) =– 4x² +5/1 +x²
The graph of f is given below. Use the graph of f to determine the given limits. Enter DNE if a limit fails to exist, except in case of an infinite limit. If an infinite limit exists, enter ∞, or -∞, as appropriate.
lim f(x)=________
x->-∞
lim f(x)=________
x->∞
![For the function f(x) = 6x2 + 2x – 4, evaluate and fully simplify each of the following.
f(x+h) =
f(x+h)-f(x)/h =](https://media.kunduz.com/media/sug-question/raw/77277295-1658845488.5771246.jpeg?w=256)
Math
FunctionsFor the function f(x) = 6x2 + 2x – 4, evaluate and fully simplify each of the following.
f(x+h) =
f(x+h)-f(x)/h =
![Given that there exists a surjective function f : S -> T, which of the following substitutions for the sets S and T are possible? Select only one answer.
(a) S = {1,2,3}. T= R.
(b) S = {x ∈ R : x² - 4 = 0}, T = {5, π, -10}
(C) S = {x ∈ R : (x² - 1)(x² - 4)=0}, T = {5,π,-10}
(d) S = {1}, T = {x ∈ R : eˣ = 0}.
(e) S = {n ∈ N : n ≤ 2022}, T={z ∈ Z : |z| ≤ 202}.](https://media.kunduz.com/media/sug-question/raw/77429756-1658844251.1666868.jpeg?w=256)
Math
FunctionsGiven that there exists a surjective function f : S -> T, which of the following substitutions for the sets S and T are possible? Select only one answer.
(a) S = {1,2,3}. T= R.
(b) S = {x ∈ R : x² - 4 = 0}, T = {5, π, -10}
(C) S = {x ∈ R : (x² - 1)(x² - 4)=0}, T = {5,π,-10}
(d) S = {1}, T = {x ∈ R : eˣ = 0}.
(e) S = {n ∈ N : n ≤ 2022}, T={z ∈ Z : |z| ≤ 202}.
![Graph the linear equation;
f(x) =8x](https://media.kunduz.com/media/sug-question/raw/77435163-1658843763.7660067.jpeg?w=256)
![Alyssa was given a gift card for a coffee a shop. Each morning, Alyssa uses the card to buy one cup of coffee. Let A represent the amount money remaining on the card after buying x cups of coffee. The table
below has select values showing the linear relationship between x and A. Determine the original amount of money on the gift card.
X A
2 15.00
4 10.00
6 5.00](https://media.kunduz.com/media/sug-question/raw/77272717-1658843735.2123673.jpeg?w=256)
Math
FunctionsAlyssa was given a gift card for a coffee a shop. Each morning, Alyssa uses the card to buy one cup of coffee. Let A represent the amount money remaining on the card after buying x cups of coffee. The table
below has select values showing the linear relationship between x and A. Determine the original amount of money on the gift card.
X A
2 15.00
4 10.00
6 5.00
![The function f(t) = 8000(0.15)^24t represents the change in a quantity over t days. What does the constant 0.15 reveal about the rate of change of the quantity?
The function is____exponentially at a rate of____ % every](https://media.kunduz.com/media/sug-question/raw/77315168-1658843261.4718409.jpeg?w=256)
Math
FunctionsThe function f(t) = 8000(0.15)^24t represents the change in a quantity over t days. What does the constant 0.15 reveal about the rate of change of the quantity?
The function is____exponentially at a rate of____ % every
![Find the domain of the function f(x) =(x^2 +2x +1)/x+1
a)Set of negative real numbers
b)Set of real numbers except -1
c)Set of real numbers except 1](https://media.kunduz.com/media/sug-question/raw/77435082-1658840275.5307157.jpeg?w=256)
Math
FunctionsFind the domain of the function f(x) =(x^2 +2x +1)/x+1
a)Set of negative real numbers
b)Set of real numbers except -1
c)Set of real numbers except 1
![Solve by graphing:
-x+y=-2
-2x+2y=-4
Select the correct answer below:
a)Infinite solutions in the form (x,-2-2)
b)Infinite solutions in the form (x,-x+2)
c)Infinite solutions in the form (x,x - 2)
d) Infinite solutions in the form (x, x+2)
e)One solution: (1, -1)
f)No solution:](https://media.kunduz.com/media/sug-question/raw/77435565-1658840255.3992126.jpeg?w=256)
Math
FunctionsSolve by graphing:
-x+y=-2
-2x+2y=-4
Select the correct answer below:
a)Infinite solutions in the form (x,-2-2)
b)Infinite solutions in the form (x,-x+2)
c)Infinite solutions in the form (x,x - 2)
d) Infinite solutions in the form (x, x+2)
e)One solution: (1, -1)
f)No solution:
![Use a graphing calculator to solve the nonlinear system.
y =e^(X+1)
X+y =1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A). The solution set is (Type an ordered pair. Use a comma to separate answers as needed. Type an integer or decimal rounded to the nearest hundred)
B). There are infinitely many solutions.
C). There is no solution.](https://media.kunduz.com/media/sug-question/raw/77221295-1658839811.3569684.jpeg?w=256)
Math
FunctionsUse a graphing calculator to solve the nonlinear system.
y =e^(X+1)
X+y =1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A). The solution set is (Type an ordered pair. Use a comma to separate answers as needed. Type an integer or decimal rounded to the nearest hundred)
B). There are infinitely many solutions.
C). There is no solution.
![Consider the function f : N→P(N) given by
f(x) = {d ∈ N: d|x}.
(a) Write out all of the elements of the set f(10) = {d ∈ N: d|x}.
(b) Is f one-to-one? Prove your answer.](https://media.kunduz.com/media/sug-question/raw/77525530-1658839418.5804222.jpeg?w=256)
Math
FunctionsConsider the function f : N→P(N) given by
f(x) = {d ∈ N: d|x}.
(a) Write out all of the elements of the set f(10) = {d ∈ N: d|x}.
(b) Is f one-to-one? Prove your answer.
![For the given function: f(x) =x-5/(x^2 -25)
A). State the domain of the given function.
B). Find the value of limx→5 f(x), if it exists. Justify your answer.
C). Find the value of limx,→∞ f(x), if it exists. Justify your answer.](https://media.kunduz.com/media/sug-question/raw/77726796-1658839105.0313573.jpeg?w=256)
Math
FunctionsFor the given function: f(x) =x-5/(x^2 -25)
A). State the domain of the given function.
B). Find the value of limx→5 f(x), if it exists. Justify your answer.
C). Find the value of limx,→∞ f(x), if it exists. Justify your answer.
![Write the equation of the exponential function represented by the table. (round each to the nearest thousandths).
X 5 3 1 -1
Y 32 16 8 4](https://media.kunduz.com/media/sug-question/raw/77287903-1658838932.3909464.jpeg?w=256)
Math
FunctionsWrite the equation of the exponential function represented by the table. (round each to the nearest thousandths).
X 5 3 1 -1
Y 32 16 8 4
![Given that
p₁ (t) = 2t² + 2t - 1 and p₂ (t) = –t² – 2t + 1,
which of the following polynomials in P₂ does not belong to span{p₁ , p₂}? Select one: :
(A) p(t) = t² - 2t + 1
(B) p(t) = 8t² + 10t -5
(C) None of these.
(D) p(t) = -7t² - 10t + 5
(E) 4t² + 2t - 1](https://media.kunduz.com/media/sug-question/raw/77751329-1658838884.2423775.jpeg?w=256)
Math
FunctionsGiven that
p₁ (t) = 2t² + 2t - 1 and p₂ (t) = –t² – 2t + 1,
which of the following polynomials in P₂ does not belong to span{p₁ , p₂}? Select one: :
(A) p(t) = t² - 2t + 1
(B) p(t) = 8t² + 10t -5
(C) None of these.
(D) p(t) = -7t² - 10t + 5
(E) 4t² + 2t - 1
![Evaluate the expression ( x⁴+7x³-2)/(y⁴+2) , when x = 4 and y=-2.
-39
39
38](https://media.kunduz.com/media/sug-question/raw/77313330-1658837905.1893806.jpeg?w=256)
![Function r(t) gives the amount of rainfall accumulated in inches, when it is t hours after the rain started. Which statement represents the meaning of the equation r(5) = 2.5 in this situation?
2.5 hours after the rain started, it has rained 5 inches
5 days after the rain started, it has rained 2.5 inches
5 hours after the rain started, it has rained 2.5 inches
It has rained 5 inches for 2.5 hours](https://media.kunduz.com/media/sug-question/raw/77272128-1658837860.9795094.jpeg?w=256)
Math
FunctionsFunction r(t) gives the amount of rainfall accumulated in inches, when it is t hours after the rain started. Which statement represents the meaning of the equation r(5) = 2.5 in this situation?
2.5 hours after the rain started, it has rained 5 inches
5 days after the rain started, it has rained 2.5 inches
5 hours after the rain started, it has rained 2.5 inches
It has rained 5 inches for 2.5 hours
![Let f(x) = (1 + 4x^2)(x - x^2).
a)Find the derivative by using the Product Rule.
f'(x) =_________
b)Find the derivative by multiplying first.
f'(x) =_________
c)Do your answers agree?
1)Yes
2)No](https://media.kunduz.com/media/sug-question/raw/77436247-1658837477.4698348.jpeg?w=256)
Math
FunctionsLet f(x) = (1 + 4x^2)(x - x^2).
a)Find the derivative by using the Product Rule.
f'(x) =_________
b)Find the derivative by multiplying first.
f'(x) =_________
c)Do your answers agree?
1)Yes
2)No
![Graph the inequality.
5x - 6y >= 0
Use the graphing tool to graph the inequality.](https://media.kunduz.com/media/sug-question/raw/77571670-1658837469.6397142.jpeg?w=256)
![Oreo was asked to find the end behavior of f(x) = 3x² +2 -7x^5+ 11. In which step did she make an error? Explain what her error was. Type your answer below.
Step 1: She found the leading coefficient to be 3x^2
Step 2: She found the coefficient to be positive 3, so the function is increasing from left to right
Step 3: She found the exponent to be even, so the ends are pointing in the same direction
Step 4: Her answer was_______](https://media.kunduz.com/media/sug-question/raw/77726211-1658836894.179747.jpeg?w=256)
Math
FunctionsOreo was asked to find the end behavior of f(x) = 3x² +2 -7x^5+ 11. In which step did she make an error? Explain what her error was. Type your answer below.
Step 1: She found the leading coefficient to be 3x^2
Step 2: She found the coefficient to be positive 3, so the function is increasing from left to right
Step 3: She found the exponent to be even, so the ends are pointing in the same direction
Step 4: Her answer was_______
![For the function, (a) determine whether it is one-to-one and (b) if it is one-to-one, find a formula for the inverse.
f(x) = 2/7x+4
Find the formula for f⁻¹(x), the inverse of f(x) = 2/7x+4 if it exists. Select the correct choice below and, if necessary, fill in any answer boxes within your choice.
A. The function is one-to-one and f⁻¹(x) = ▢.
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
B. The function is not one-to-one and there is no inverse function.](https://media.kunduz.com/media/sug-question/raw/77729984-1658836755.956079.jpeg?w=256)
Math
FunctionsFor the function, (a) determine whether it is one-to-one and (b) if it is one-to-one, find a formula for the inverse.
f(x) = 2/7x+4
Find the formula for f⁻¹(x), the inverse of f(x) = 2/7x+4 if it exists. Select the correct choice below and, if necessary, fill in any answer boxes within your choice.
A. The function is one-to-one and f⁻¹(x) = ▢.
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
B. The function is not one-to-one and there is no inverse function.
![Evaluate f(3).
f(x) = -x+3 if x < 2
2x-3 if x ≥ 2
A) f(3) = 0
B) f(3) = 6
C) undefined
D) f(3) = 3](https://media.kunduz.com/media/sug-question/raw/77876417-1658836729.08544.jpeg?w=256)
Math
FunctionsEvaluate f(3).
f(x) = -x+3 if x < 2
2x-3 if x ≥ 2
A) f(3) = 0
B) f(3) = 6
C) undefined
D) f(3) = 3
![Solve the equation by factoring: (x + 4)(x + 5) = 11x + 68
x=
Write your answers as a list of integers or reduced fractions, with your answers separated by (a) comma(s). For example, if you get 4 and-2/3 as your answers, then enter 4,-2/3 in the box.](https://media.kunduz.com/media/sug-question/raw/77323861-1658836459.4357343.jpeg?w=256)
Math
FunctionsSolve the equation by factoring: (x + 4)(x + 5) = 11x + 68
x=
Write your answers as a list of integers or reduced fractions, with your answers separated by (a) comma(s). For example, if you get 4 and-2/3 as your answers, then enter 4,-2/3 in the box.
![Consider the function f(x) = 3x^5/3 + 60x^2/3.
(a) Show that f'(x) = {[5(x + 8)] / ∛x}. Then find and classify all local extrema of f.
b) Find the values of the global extrema of f on the domain [-1,1].
c) Justify briefly, but precisely, why f has global extrema on the interval [-1, 1]](https://media.kunduz.com/media/sug-question/raw/77914624-1658831057.2986515.jpeg?w=256)
Math
FunctionsConsider the function f(x) = 3x^5/3 + 60x^2/3.
(a) Show that f'(x) = {[5(x + 8)] / ∛x}. Then find and classify all local extrema of f.
b) Find the values of the global extrema of f on the domain [-1,1].
c) Justify briefly, but precisely, why f has global extrema on the interval [-1, 1]
![For the given functions f and g, find the requested function and state its domain.
f(x) = 9x - 2; g(x) = 7x - 8.
Find f-g.
(f - g)(x) = 2x + 6; all real numbers
(f - g)(x) = 2x - 10; {x|x ≠ 5}
(f - g)(x) = -2x - 6; all real numbers
(f - g)(x) = 16x - 10; {x|x ≠ 1}](https://media.kunduz.com/media/sug-question/raw/77876638-1658830881.1994655.jpeg?w=256)
Math
FunctionsFor the given functions f and g, find the requested function and state its domain.
f(x) = 9x - 2; g(x) = 7x - 8.
Find f-g.
(f - g)(x) = 2x + 6; all real numbers
(f - g)(x) = 2x - 10; {x|x ≠ 5}
(f - g)(x) = -2x - 6; all real numbers
(f - g)(x) = 16x - 10; {x|x ≠ 1}
![Isaac invested $1,800 in an account paying an interest rate of 4.7% compounded
continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 15 years?](https://media.kunduz.com/media/sug-question/raw/77730821-1658830239.1889257.jpeg?w=256)
Math
FunctionsIsaac invested $1,800 in an account paying an interest rate of 4.7% compounded
continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 15 years?
![Let T: P₃->P₃, be the linear transformation such that
T(2x²) = -2x² + 3x. T(-0.5x - 2) = -4x² - 4x -2, T(5x² + 1) = 2x - 1.
Find T(1), T(x), T(x²), and T(ax² + bx + c), where a, b, and c are arbitrary real numbers.
T(1) =
T(x) =
T(ax² + bx + C) =](https://media.kunduz.com/media/sug-question/raw/77913411-1658829880.6973152.jpeg?w=256)
Math
FunctionsLet T: P₃->P₃, be the linear transformation such that
T(2x²) = -2x² + 3x. T(-0.5x - 2) = -4x² - 4x -2, T(5x² + 1) = 2x - 1.
Find T(1), T(x), T(x²), and T(ax² + bx + c), where a, b, and c are arbitrary real numbers.
T(1) =
T(x) =
T(ax² + bx + C) =
![Calculate the average rate of change of the following functions.
1. f(x) = x² over the interval 2 ≤ x ≤ 3
2. h(x) = 7 - 3x² over the interval 2 ≤ x ≤ 5
Criteria for Success
The difference f(x2)-f(x1) is calculated.
The difference (x2) - (x1) is calculated.
Final answer is expressed with correct units.](https://media.kunduz.com/media/sug-question/raw/77932833-1658829196.8034399.jpeg?w=256)
Math
FunctionsCalculate the average rate of change of the following functions.
1. f(x) = x² over the interval 2 ≤ x ≤ 3
2. h(x) = 7 - 3x² over the interval 2 ≤ x ≤ 5
Criteria for Success
The difference f(x2)-f(x1) is calculated.
The difference (x2) - (x1) is calculated.
Final answer is expressed with correct units.
![The equation below shows the cost C in dollars, of a small company to produce units in one week. C(x) = 500 + 60x +0.5x^2? How much money will it cost to produce 28 units in one week?](https://media.kunduz.com/media/sug-question/raw/77726307-1658828808.359487.jpeg?w=256)
Math
FunctionsThe equation below shows the cost C in dollars, of a small company to produce units in one week. C(x) = 500 + 60x +0.5x^2? How much money will it cost to produce 28 units in one week?
![Graph an exponential that passes through the point (2,6) and has growth factor 3. Plot and label at least 3 other points (include an intercept).](https://media.kunduz.com/media/sug-question/raw/77807546-1658784506.1445746.jpeg?w=256)
Math
FunctionsGraph an exponential that passes through the point (2,6) and has growth factor 3. Plot and label at least 3 other points (include an intercept).
![A certain radioactive element has a half-life of 35 days. If you had a 100 grams of this element, the mass m of the element after t 35- day intervals is represented by m= 100(0.5)t. Find the approximate daily decay rate of this element.
a. 98.0%
b. 17.5%
c. 2.0%
d. 1.4%](https://media.kunduz.com/media/sug-question/raw/77727286-1658746686.97944.jpeg?w=256)
Math
FunctionsA certain radioactive element has a half-life of 35 days. If you had a 100 grams of this element, the mass m of the element after t 35- day intervals is represented by m= 100(0.5)t. Find the approximate daily decay rate of this element.
a. 98.0%
b. 17.5%
c. 2.0%
d. 1.4%
![Find the domain of the composite function f₀g.
f(x) = x + 4; g(x) = 5/x+6
{x | x is any real number}
{x | x ≠ -6}
{x| x ≠ -10)
{x | x≠ -6, x ≠ -4}](https://media.kunduz.com/media/sug-question/raw/77876719-1658745391.1214967.jpeg?w=256)
Math
FunctionsFind the domain of the composite function f₀g.
f(x) = x + 4; g(x) = 5/x+6
{x | x is any real number}
{x | x ≠ -6}
{x| x ≠ -10)
{x | x≠ -6, x ≠ -4}
![Let f(x)=x²-9 and g(x) = 6 -x. Perform the composition or operation indicated.
(fg)(-1)](https://media.kunduz.com/media/sug-question/raw/84647648-1658674019.9067833.jpeg?w=256)
Math
FunctionsLet f(x)=x²-9 and g(x) = 6 -x. Perform the composition or operation indicated.
(fg)(-1)
![(b) Find the coordinates of the vertex.
(c) Find the intercept(s).
For both the x- and y-intercept(s), make sure to do the following. If there is more than one, separate them with commas. .If there are none, select "None".
x-intercept(s):
y-intercept(s):
(d) Find the equation of the axis of symmetry. equation of axis of symmetry:](https://media.kunduz.com/media/sug-question/raw/82678679-1658667005.3859112.jpeg?w=256)
Math
Functions(b) Find the coordinates of the vertex.
(c) Find the intercept(s).
For both the x- and y-intercept(s), make sure to do the following. If there is more than one, separate them with commas. .If there are none, select "None".
x-intercept(s):
y-intercept(s):
(d) Find the equation of the axis of symmetry. equation of axis of symmetry:
![Solve by any method.
6x - 8y = -0.6
3x + 2y = 0.9](https://media.kunduz.com/media/sug-question/raw/83885104-1658664826.7364006.jpeg?w=256)
![Write the equation in standard form and enter it below. Do not enter blank spaces in your answer.
y=3/4 x+2
Standard form of equation:](https://media.kunduz.com/media/sug-question/raw/84622019-1658663801.1128073.jpeg?w=256)
Math
FunctionsWrite the equation in standard form and enter it below. Do not enter blank spaces in your answer.
y=3/4 x+2
Standard form of equation:
![Let f(x) = 3x² - 8x + 5 and g(x) = x² + 16. Find ƒ + g, ƒ − g, f · g, and Simplify your answers.
1. f + g =
2. f-g=
3. f . g =
4. f/g =](https://media.kunduz.com/media/sug-question/raw/84565854-1658663632.1855395.jpeg?w=256)
Math
FunctionsLet f(x) = 3x² - 8x + 5 and g(x) = x² + 16. Find ƒ + g, ƒ − g, f · g, and Simplify your answers.
1. f + g =
2. f-g=
3. f . g =
4. f/g =
![The function P(t) = 37.25e0.0096t. approximates the population, in millions, of California t years since 2010. Assuming this trend continues, approximate the number of years it will take California's population to reach 50 million. Round your answer to two decimal places.](https://media.kunduz.com/media/sug-question/raw/84570310-1658662902.4256115.jpeg?w=256)
Math
FunctionsThe function P(t) = 37.25e0.0096t. approximates the population, in millions, of California t years since 2010. Assuming this trend continues, approximate the number of years it will take California's population to reach 50 million. Round your answer to two decimal places.
![If the point (5,-2) is on the graph of a function that is shifted to the right by 3, what point is on the new graph?
(5, 1)
(8.1)
(8,-2)
(2,-2)](https://media.kunduz.com/media/sug-question/raw/84587604-1658662744.4659135.jpeg?w=256)
Math
FunctionsIf the point (5,-2) is on the graph of a function that is shifted to the right by 3, what point is on the new graph?
(5, 1)
(8.1)
(8,-2)
(2,-2)
![Solve each equation
a) Solve x2/3 - 5x¹/3 +6=0
b) Solve p4-3p2-4 = 0
c) Solve x² - 4x-1-5 = 0](https://media.kunduz.com/media/sug-question/raw/84590233-1658661593.953603.jpeg?w=256)
Math
FunctionsSolve each equation
a) Solve x2/3 - 5x¹/3 +6=0
b) Solve p4-3p2-4 = 0
c) Solve x² - 4x-1-5 = 0
![Which of the following represents the rectangular equation x² + y² + 5x - 3y = 0 in polar form?
r= -5sin θ + 3cos θ
r= -3sin θ+ 5cos θ
r=3sin θ- 5cos θ
r= 5sin θ- 3cos θ](https://media.kunduz.com/media/sug-question/raw/84598670-1658661129.5171762.jpeg?w=256)
Math
FunctionsWhich of the following represents the rectangular equation x² + y² + 5x - 3y = 0 in polar form?
r= -5sin θ + 3cos θ
r= -3sin θ+ 5cos θ
r=3sin θ- 5cos θ
r= 5sin θ- 3cos θ
![Find the inverse function of y = g(x) = 5x³ + 1
g-¹(y) =](https://media.kunduz.com/media/sug-question/raw/84599262-1658661033.9899418.jpeg?w=256)
![Check that the functions f(x) = e2x and g(x)=In(x)/2 are inverses using algebra.](https://media.kunduz.com/media/sug-question/raw/84599327-1658660857.2794383.jpeg?w=256)
![A polar curve is represented by the equation r₁ = 2 + 3cosθ.
Part A: What type of limaçon is this curve? Justify your answer using the constants in the equation.
Part B: Is the curve symmetrical to the polar axis or the line θ = π/2? Justify your answer algebraically.](https://media.kunduz.com/media/sug-question/raw/84599187-1658660727.2811217.jpeg?w=256)
Math
FunctionsA polar curve is represented by the equation r₁ = 2 + 3cosθ.
Part A: What type of limaçon is this curve? Justify your answer using the constants in the equation.
Part B: Is the curve symmetrical to the polar axis or the line θ = π/2? Justify your answer algebraically.
![Decompose the function y = 2x+1 into u(v(x)). If we assume u(x) = 2x, what is v(x)?](https://media.kunduz.com/media/sug-question/raw/84599315-1658660642.8088686.jpeg?w=256)
![Suppose f(q) = C = 200+ 0.1q gives the cost, C, in dollars to manufacture q kg of a chemical.
Find and interpret f-¹(C).](https://media.kunduz.com/media/sug-question/raw/84599337-1658660586.824114.jpeg?w=256)
Math
FunctionsSuppose f(q) = C = 200+ 0.1q gives the cost, C, in dollars to manufacture q kg of a chemical.
Find and interpret f-¹(C).
![a) Find and classify the critical point(s).
b) Find the interval(s) where f(x) is increasing.
c) Find the interval(s) where f(x) is decreasing.
1. f(x)=x²-x-1
2. f(x)=2x^4 - 4x² +1
3. f(x)=xe^1/x](https://media.kunduz.com/media/sug-question/raw/74729281-1658594218.9056423.jpeg?w=256)
Math
Functionsa) Find and classify the critical point(s).
b) Find the interval(s) where f(x) is increasing.
c) Find the interval(s) where f(x) is decreasing.
1. f(x)=x²-x-1
2. f(x)=2x^4 - 4x² +1
3. f(x)=xe^1/x