Functions Questions and Answers

Approximate each number using a calculator. (a) 173.14 (b) 173.141 (a) 173.14 (c) 173.1415

The function f(x)=3√x^5 + 6 is one-to-one. (a) Find the inverse of f and check the answer. (b) Find the domain and the range of f and f-1 (a) f-¹(x)= (Simplify your answer.)

The function f(x) =6x/x+5 is one-to-one. (a) Find its inverse and check your answer. (b) Find the domain and the range of f and f-1. (a) f-¹ (x)= (Simplify your answer.)

Suppose that it is given to you that f'(x) = (x+4) (6- x)(7- x) Then the first relative extremum (from the left) for f(x) occurs at x = The function f(x) has a relative [ at this point. The second relative extremum (from the left) for f(x) occurs at x = The function f(x) has a relative? ✓at this point. The third relative extremum (from the left) for f(x) occurs at x = The function f(x) has a relative? at this point. The first inflection point (from the left) for f(x) occurs at x = The second inflection point (from the left) for f(x) occurs at a =

Graph f(x) = -4log6(x + 5) + 3 using transformations by first graphing the basic logarithmic function (parent function), then the progression of transformations (in the correct order). Show at least two points. Identify the following: a. Domain b. Range c. Vertical Asymptote d. End behavior

Assume that a normal distribution has a mean of 20 and a standard deviation of 6. What percentage of the values in the distribution do we expect to fall between 14 and 20? OA. 17% OB. 25% O C. 68% OD. 34% *****

Determine the domain of the function. g(x) = 4√/1-x What is the domain? (Type in interval notation.)

Find |x| when x = 15 and x = - 15. Both values are - 15. |15| = 15 and | - 15| = - 15 |15| = - 15 and | - 15| = 15 Both values are 15.

4 1 point The polynomial f (x) = -2x (x-4)² (x - 5) is graphed in the coordinate plane. Which statement is correct about the graph? As a ▷ ∞o, f(x) ▷ ∞ and as a ▷ -∞, f (x) > -∞ O As xD ∞o, f (x) ▷ -∞ and as ▷ -∞, f (x) > ∞ O As Doo, f (x) ► -∞ and as a ▷ -∞, f (x) ▷ -∞ O As Doo, f(x) > ∞ and as a ▷ -∞, f (x) > ∞

Use a calculator with a key or a key to solve the following. The exponential function f(x)=576(1.032)* models the population of a country, f(x), in millions, x years after 1969. Complete parts (a)-(e). a. Substitute 0 for x and, without using a calculator, find the country's population in 1969. The country's population in 1969 was 576 million. b. Substitute 22 for x and use your calculator to find the country's population, to the nearest million, in the year 1991 as modeled by this function. The country's population in 1991 was 1152 million. c. Find the country's population, to the nearest million, in the year 2013 as predicted by this function. The country's population in 2013 will be 2303 million. d. Find the country's population, to the nearest million, in the year 2035 as predicted by this function. The country's population in 2035 will be million.

Which set of ordered pairs does not represent a function? O {(-8,-8), (9, -9), (4, 5), (4,0)} O {(5,-5), (-7, 3), (9, 3), (3,-9)} O {(-5,0), (3, -6), (5,3), (-6,3)} O {(-9, -2), (0, 8), (-2,-2), (8,9)}

Assume that a normal distribution has a mean of 27 and a standard deviation of 4. What percentage of the values in the distribution do we expect to fall below 19? A. 5% B. 25% C. 2.5% D. 17%

The force of the wind blowing on a vertical surface varies jointly as the area of the surface and the square of the velocity. If a wind of 20 mph exerts a force of 10 lb on a surface of ft², how much force will a wind of 30 mph place on a surface of 2 ft²?

Sketch a function on the graph below, and sketch its inverse. The function doesn't need to be complex or amazingly well-drawn, but it should be clear that you know how to visually take the inverse of a function. X

Henry is buying bagels for a family gathering. Each bagel costs $0.75. Answer the questions below regarding the relationship between the total cost and the number of bagels purchased.

Find the vertical asymptotes and holes for the graph of the rational function. y=(x + 7)(x - 1)/(x - 1)(x + 3) Identify any vertical asymptotes for the graph of the function. Select all that apply. A. x = -7 B. x = 1 C. x = -3 D. x = 0

Begin by graphing f(x)= log x. Use transformations of this graph to graph the given function. Graph and give the equation of the asymptote. Use the graphs to determine the function's domain and range. h(x) = log x-6 Determine the transformations that are needed to go from f(x)= log x to the given graph. Select all that apply. A. shrink horizontally B. stretch vertically C. shift 6 units to the right D. stretch horizontally E. shift 6 units to the left F. reflect about the x-axis G. shrink vertically H. shift 6 units downward I.shift 6 units upward J. reflect about the y-axis

Solve the equation. r-14=23

Which set of words describes the end behavior of the function f(x) = 0.4(2x-9)(3x + 1)(x-7)(x+9)? Select the correct answer below: rising as x approaches negative and positive infinity O falling as x approaches negative and positive infinity O rising as x approaches negative infinity and falling as x approaches positive infinity falling as x approaches negative infinity and rising as x approaches positive infinity

Find the largest open intervals on which the function is concave upward or concave downward, and find the location of any points of inflection. f(x) = -5x²-3x-1 ***** Select the correct choice below and fill in the answer box(es) to complete your choice. (Type your answer in interval notation. Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression.) OA. The function is concave upward on and concave downward on OB. The function is concave downward on OC. The function is concave upward on Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The point(s) of inflection is/are at (Type an ordered pair. Use a comma to separate answers as needed.) B. There is no point of inflection. The function never has an interval that is concave upward/downward. The function never has an interval that is concave upward/downward.

f(x) = For each function h given below, find a formula for h(z) and the domain of h. Note: When entering interval notation in WeBWork, use I for oo, -I for -00, and U for the union symbol. If the set is empty, enter "0" without the quotation marks... (A)h(z) = (fog)(1). h(z)= (1/x)(2x^3-2x) Domain= (B) h(z) = (gof)(z). h(z) = Domain= (C) h(z) = (fof)(z). h(z) = Domain= (D) h(z) = (gog)(z). h(z) = and g(x) = 2x³ - 2z. Domain=

Select the statement that correctly describes the end behavior of f(x) = 8 - 2x² + 4x³. As x gets larger and larger in either the positive or negative direction, f(x) gets larger and larger in the positive direction. As x gets larger and larger in the positive direction, f (x) gets larger and larger in the positive direction. As x gets larger and larger in the negative direction, f (x) gets larger and larger in the negative direction. As x gets larger and larger in either the positive or negative direction, f (x) gets larger and larger in the negative direction. As x gets larger and larger in the positive direction, f (x) gets larger and larger in the negative direction. As x gets larger and larger in the negative direction, f (x) gets larger and larger in the positive direction.

Find a so that the graph of f(x) = log ax contains the point (19,2). ***** a = (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression)

Which of the following are exponential functions? Select all correct answers. Select all that apply: j(x) = 12(8)x h(x) = 14(4.9)x f(x) = 9(2/3)x g(x) = 11(-4)x k(x) = 6(−1)x

Determine the vertical asymptote(s) of the function. If none exists, state that fact. 3x - 7 x-6 f(x) = Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. OA. The function has three vertical asymptotes. The leftmost asymptote is (Type equations.) OB. The function has one vertical asymptote, (Type an equation.) OC. The function has two vertical asymptotes. The leftmost asymptote is (Type equations.) OD. The function has no vertical asymptotes. the middle asymptote is and the rightmost asymptote is and the rightmost asymptote is

Given f(x) = 7x and g(x) = 5x² +6, find the following expressions. a) (fog)(4) (b) (gof)(2) (c) (fof)(1) (d) (gog)(0)

A factory produces widgets and zurls. The combined number of widgets and zurls made each day cannot be more than 12. The maximum number of widgets the factory can produce in a day is 4. Let x be the number of widgets and y the number of zurls. Select all the inequalities that represent this situation. a. x < 4 b. x ≤ 4 C. x > 4 d. x + y > 12 e. x + y ≤ 12

Given f(x) = 5x and g(x)= 8x² + 1, find the following expressions. (a) (fog)(4) (b) (gof)(2) (c) (fof)(1) (d) (gog)(0) (a) (fog)(4) = (b) (gof)(2) = (c) (fof)(1) = (d) (gog)(0) =

For f(x) = 4x + 4 and g(x) = 6x, find the following composite functions and state the domain of each. (a) fog (b) gof (c) fof (d) gog (a) (fog)(x) =

An object with initial temperature 160° F is submerged in large tank of water whose temperature is 70°F . Find a formula for F(t), the temperature of the object after t minutes, if the cooling constant is k = 1.2

Mary sells homemade jewelry through an online shop. She found that each time she increases the price of each necklace by $2, she sells three fewer necklaces per week. Mary generally charges $12 for each necklace, and she typically sells 30 necklaces per week. The factored form of the equation below represents the revenue, R(x), after x price increases of $2. R(x) (12 +21) (30-31) Which of the following is the correct interpretation of the y-intercept in the given situation? The y-intercept represents the 10 necklaces Mary sells in order to break even. The y-intercept represents Mary's maximum revenue of $384. The y-intercept represents Mary's revenue of $360 before any price increases. The y-intercept represents the $12 price per necklace Mary initially charges.

Spinelli/Ninan EXTRA CREDIT due wed! 1. What is the equation of a line passing through the point (5, -3) and parallel to the line whose equation is 4y - x = 8?

1. Devin is selling small bags of cookies at a fundraiser for $1.25 each. If the amount of money he makes, m, selling b bags of cookies is modeled using a function, then determine whether $10.00 could be a member of this function's range.

For f(x) = 4x+4 and g(x) = 6x, find the following composite functions and state the domain of each. (a) fog (b) gof (c) fof (d) gog (a) (fog)(x) = 24x +4 (Simplify your answer.) Select the correct choice below and fill in any answer boxes within your choice. .... OA. The domain of fog is {x} (Type an inequality. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The domain of fog is all real numbers. (b) (gof)(x) = (Simplify your answer.)

Question If the function y = = e is vertically compressed by a factor of 3, reflected across the y-axis, and then shifted down 2 units, what is the resulting function? Write your answer in the form y = ceax+b. -2x Provide your answer below: y =

Consider the following function. 1 (x+4)² Step 1 of 2: Determine the more basic function that has been shifted, reflected, stretched, or compressed. Answer g(x) = - 2/15 Correct f(x) =

After its fastest rate of growth ever during the 1980s and 1990s, the rate of growth of world population is expected to slow dramatically in the twenty-first century. The function G(t) = 1.58e-0.213t gives the projected annual average percent population growth per decade in the tth decade, with t= 1 corresponding to 2000. (Source: U.S. Census Bureau.) (a) What will the projected annual average population growth rate be in 2030? (Round your answer to two decimal places.) (b) How fast will the projected annual average population growth rate be changing in 2030? (Round your answer to two decimal places.)

Consider the graph of the function f(x) = (x-5)(x-12) / (x+3)(x-2)(x-5) What is the y-intercept? Write your answer in the form (x, y) and use fractions if necessary.

Consider the function below. (If an answer does not exist, enter DNE.) f(x) = e²x + e-x (a) Find the interval(s) on which f is increasing. (Enter your answer using interval notation.) Find the interval(s) on which fis decreasing. (Enter your answer using interval notation.) (b) Find the relative minimum value(s) of f. (Enter your answers as a comma-separated list.) (c) Find the interval(s) on which fis concave up. (Enter your answer using interval notation.)

Sketch the graph of the function. Identify any local extrema and points of inflection. f(x) =x-4/x+3 What are the coordinates of the relative maxima? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. (Simplify your answer. Type an ordered pair. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed B. There is no maximum.

Given that the polynomial f(x) has 8 x-intercepts, which of the following most accurately describes the degree of f(z)? Select the correct answer below: The degree of f(x) is at least 8. The degree of f(x) is at least 7. The degree of f(x) is at most 7. The degree of f(2) is at most 9. The degree of f(x) is at most 8.

Given that the polynomial f(x) has degree 8, which of the following most accurately describes the number of turning points of f(x)? Select the correct answer below: The graph of f(x) has at most 7 turning points. The graph of f(x) has at least 9 turning points. The graph of f(x) has at most 8 turning points. The graph of f(x) has at least 8 turning points. The graph of f(x) has at most 9 turning points. The graph of f(x) has at least 7 turning points.

Consider the function f(x) = x³ + 16x² + 60x + 40. If there is a remainder of -5 when the function is divided by (x - a), what is the value of a? Select the correct answer below: -1 1 -2 2

Find the inverse of the function f(x) = 2x³ + 5. Provide your answer below: f-¹(x) =

Use synthetic division to find the result when x4-2x² - 4x48 is divided by x - 3. Write your answer in the form q(x) +r(x)/d(x) where g(x) is the quotient, r(x) is the remainder, and d(x) is the divisor.

Consider the function: f(x) = -5x³ + 120x² + 3x - 1 Determine the intervals on which the function is concave upwards or concave downwards.

Correct The safe load, L, of a wooden beam supported at both ends varies jointly as the width, w, and the square of the depth, d, and inversely as the length, L. A wooden beam 3 in. wide, 9 in. deep, and 3 ft long holds up 41671 lb. What load would a beam 4 in. wide, 4 in. deep, and 20 ft. long, of the same material, support? Round your answer to the nearest integer if necessary. Answer pounds Keypad Keyboard Shortcuts

Find the domain of the function f(x)= x²-16 x²-4 Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choi O A. The domain is {x}. (Simplify your answer. Type an inequality. Use a comma to separate answers as needed.) OB. The domain is {x|xz x# }. (Simplify your answer. Use a comma to separate answers as needed.) OC. The domain is {x|x* }. (Simplify your answer. Use a comma to separate answers as needed.) OD. The domain is {x|x≤ x#}. (Simplify your answer. Use a comma to separate answers as needed.) OE. The domain is the set of all real numbers.

Consider the function: f(x) = 5x³ + 120x² + 3x - 1 Step 2 of 2: Locate any points of inflection. Enter your answer as (x, y)-pairs. AnswerHow to enter your answer (opens in new window) 3 Points Separate multiple entries with a comma. Keypad Keyboard Shortcut Selecting a radio button will replace the entered answer value(s) with the radio button value. If the radio button is not selected, the entered answer is used.

Based on the degree of the polynomial f(x) given below, what is the maximum number of turning points the graph of f(x) can have? f(x) = (x²-7) (x² − 6) (x²+4)