Functions Questions and Answers

An exponential function contains the points (1,0.9) and (2, 1.62). What is an exponential function that contains these points? y 0.5 * 1.8" y=2*0.9² y = 0.5 * 0.92 y = 0.9

An exponential function contains the points (2,16/3) and (3, 64/9) What is an exponential function that contains these points? Select one: y=(3/4)* y=3*4^x y = 4^x y=3* (4/3)^x

Let f(x)=1/x. What is the value of f(1/100)

Factor each polynomial completely. If a polynomial cannot be factored, write "prime". a) t² + 4t - 12 List possible combinations: Factored form: b) a²-a-12 List possible combinations: Factored form:

f (x) is transformed from y =x^3 by shift 1 units to the right, reflect about the y-axis, vertical stretch by a factor of 2, and shift 3 units up. Find the equation for f(x) f(x) = 2 (-2+3)³ +1 f(x) = -2(x+3)³ + 1 f(x)=2(-x-1)³ +3 f(x) = -2(x+1)³ +3 f(x) = -2(x-1)³ +3 f(x) = 2 (-x+1)³ +3

Determine whether the following function is even, odd, or neither. f(x) = 2x² - 3

A table for f (x) is given below. x -4 -2 0 2 4 f(x) 5 6 8 10 14 Complete the following tables. [Hint: Be sure to list the x values from least to greatest.] x A B C D E h(x)=f(x-3) F G H I J A= B= C= D= E= F= G= H= I= J=

Let f(x) = 4x-6 and g(x) = 5x². Find the domain of (f+g)(x). Select one: a. The domain of f + g is the set of all real numbers except x = 0. b. The domain of f + g is the set of all x ≤0. c. The domain off + g is the set of all x ≥ 0. d. The domain of f + g is the set of all real numbers.

What is the average value of f(x) between x = 0 and x = 2 for f(x) =2/2x+1 1.609 0.805 0.693 0

Find the inverse function of f(x) = x² - 4x-5, x ≥ 2. Show that the functions are inverse functions of each other, using the definition below:

For the following function, find the value of (a) f(-1) and (b) f(3), if possible. y= x²-2 if x ≤0 x³ +4 if x > 0 (a) Select the correct choice below and, if necessary, fill in the answer box to complete your answer. A. f(-1) = B. There is no solution. (Simplify your answer.)

For the following functions: answer the all these a. Find domain and range b. Find slope and intercepts c. Find average rate of change d. Graph. f(x)= 2x/3 +1 g(x) = -x/3 -1 h(x) = -3x/4 +5

Which of the following is not a function? a) y=x² b)x=y³ c) 2x + 3y = 5 d) x² + y² = 1

Which of the following statements is/are true about the function f(x) = - 5|x| +4x³. f(x) is an odd function. The graph of f(x) exhibits symmetry with respect to y axis. The graph of f(x) exhibits symmetry with respect to origin. f(x) is an even function. None of the other statements are true because f(x) is neither even nor odd.

Consider the functions below. f(x) = x/(x-4) g(x) = 9/x (a) Compute (fog)(x). Be careful when you input compound fractions. (fog)(x) = (b) Determine the domain of f o g. all real numbers except 0 and 4 all real numbers all real numbers except 9/4 all real numbers except 0 and 9/4 (c) Compute (gof)(x). Be careful when you input compound fractions. (gof)(x) = (d) Determine the domain of f o g. all real numbers all real numbers except 0 and 9 all real numbers except 0 all real numbers except 0 and 4

8. (Piecewise functions) Since each piece of a piecewise function is only graphed for part of the domain, we usually don't get the whole shape for each piece. Show what each shape looks like when it is cut off by the given domain. Make sure to determine if endpoints should be open circles or closed circles. The first and last are done for you as examples. a) y = (x + 2)², if x < -2 b) y = x, if - 2 ≤ x < 2 c) y = √x-1, if x ≥ 2

Use the pair of functions to find f (g (0)). f(x) = 4x+5, g(x) = 7=x²

Evaluate the expression 3f (3) - 2g (-4) for the given functions f and g. f(x) = 5x - 2 g(x) = 5-x² 3f (3) - 2g (-4)=

Use the given functions to find g (f(x)). f(x) = x² +3 and g(x) = √x +3 g (f(x)) = Use sqrt(x) to enter a square root of x.

Use the given functions to find g (f(x)), and give the restrictions on x f(x)=1/x-2 and g(x)= 3/x +2 g (ƒ (x)) = where x ≠

Suppose f(x)=1/x and g(x)=x-8. Also, suppose h(x) = f(g(x)). Then h(x) = 1/x-8. Find the domain of h (x) =1/x-8 Express the domain using inequality notation.

Find the domain of the function. v(x)=√x-7 Write your answer using interval notation.

More on Polynomials:Question 9 Given that p (-3) = 0, p (1) = 0, and p (2) = 0, which expression could be p (x)? -x³ - 2x² - 7x+6 x³ + 2x² + 7x-6 x³ + x² - 7x+6 x³-7x+6

Janis divided the two polynomials shown. (8x² - 10x-129)/(4x + 3) What is the quotient? 2x-1+(-15/(4x+3)) 2x-1+(-9/(4x+3)) 2x+4 2x-4

Which of the following statements is true about this function? Select one: f(x) =1/x f(x) is even f(x) is odd We cannot determine whether f(x) is even or odd f(x) is both even and odd f(x) is neither even nor odd

use the graphical method to locate the roots of f(x) = 5 cos(3x) - 2 sin(x) between x = 1 and x =6

The number of females in science continues to show steady increases. The number of female researchers in a certain country can be modeled by the function F(x) = 0.632x^1.566 where x is the number of years after 1940 and F(x) is the number of female researchers in thousands. a. What type of function is this? b. What is F(20)? What does it mean? c. How many female researchers will there be in 2030? a. F(x) = 0.632x^1.566 is a_________function.

Use the given functions to find g (f (x)), and give the restrictions on . f(x) = 1/x-3and g(x) = 4/x +3 g (f(x)) where x ≠

Use the given functions to find f (g(x)), and give the restrictions on a. f(x) = 1/x-4 and g(x) = 4/x + 4 f(g(x)) = where x ≠

f(x) = −(x + 7)² – 1 Domain of f: Range of f:

g(x)=x² - 2x - 3 Domain of g: Range of g:

f(x)=(x-8)² - 7 Domain of f: Range of f:

h(x) = 2x²-3x - 9 Domain of h: Range of h:

h(x) = 2x² - 2x +9 Domain of h: Range of h:

Let the polynomial function g be a function of x. The graph of the polynomial has four zeros at -5, -3/4,0, 7. Select all the expressions that could represent g: a. -4x(x + 5) (4x + 3)(x-7) b. -4x(x + 5) (4x+3)(x-7)² c. 4x(x - 5)(x+3)(x+7) d. 4x(x + 5) (3x - 4)(x-7) e. -x(x + 5) (x+³)(x-7)

Find the domain of f (x) = 2x − 1 O (-∞, 0) U (0, ∞) 0 (-∞, ∞) 0 (-∞, -¹) U ( 1/2, ∞) 0 (-∞,-1/2) U (-1/2,∞)

Find functions f and g such that (fog) = 2√x + 5.

Let f (x) 2-3 and g(x) = ² + 4. a. Find and simplify (fog)(x). (fog)(x) = b. Find the restriction for the domain of (fog)(x) Domain restriction: (If there's more than one values, separate each value using comma.)

Does the relation represent y as a function of x? 2x=5y+3/(9y- 4) No because there are values of x that correspond to more than one value of y. Yes because each value of x corresponds to exactly one value of y. Yes because the relation is described by an equation containing x and y. No because the equation is not solved for y.

Let f (x) be defined as shown below. Find ƒ (−2), ƒ (0), ƒ (2). 3 if x ≤0 f(x) = (4x-1 if x > 0 f(-2)= f (0) f(2)=

Find the domain of f (x) = √4 – x. (4,∞) (4,∞) (-∞,4] (-∞,4) [4, ∞) (-∞, 4) U (4, ∞) (-∞,∞)

Consider h(w) = (w +9) (w+4) (w + 1) on [-9, -1]. Determine the interval over which h is continuous and the interval over which h is differentiable. h is continuous on_________ h is differentiable on___________

Consider f(x) = 6 + (− 9x² - 18x) e^x on [ - 2, 0]. Determine the interval over which f is continuous and the interval over which f is differentiable. f is continuous on__________ f is differentiable on_______

If f(x) = 3x - 9 and g(x) = -x² find the following: a. f(-2)

For the real-valued functions g(x)=x²-1 and h(x)=√x+6, find the composition go and specify its domain.

Let f(x) = 3x - 1 and g(x) = 2x². Perform the function operation and then find the domain of the result. (f+g)(x)

5. Find the inverse of each function. Is the inverse a function? a. f(x) = x³ b. f(x) = √2x-1 +3

Let f(x) = x - 1 and g(x) = x². Perform the function operation and then find the domain of the result. (f - g)(x)

Find the parent function for each graph below. Then describe the transformations that occurred to get each function below. a. y = -√16x + 32 b. y =3√8x - 24 + 1

4. Let g(x) = 2x and h(x) = x² + 4 a. (hog)(2) b. (goh)(-2) c. (hoh)(x)