Functions Questions and Answers

Use graphing technology to find the range of the function f(x) = (1/2)ª – 1.

Consider the following relation. y=x+1 Find four points contained in the inverse. Express your values as an integer or simplified fraction.

Bill is a software salesman. His monthly salary is $2500 plus an additional $50 for every copy of Math is Fun he sells. Let S represent his total salary this month (in dollars), and let N represent the number of copies of Math is Fun he sells. Write an equation relating Sto N, and then graph your equation using the axes below.

Which of the following is true? For a pair of functions to be inverses, their compositions must be equal to 1. In an inverse relation, coordinates of the ordered pairs are multiplied by 2. The horizontal line test is used to determine if a function's inverse will be a function. An inverse of a function is always a function.

Consider the following function on the given domain. 1/15 Correct f(x) = (x-2)-2x22 Step 2 of 2: Find the domain of the inverse function, f(x). Express your answer as an inequality. Answer

Consider the function f(x) = (x + 2)² + 1. Which of the following functions shifts the graph of f(x) to the right three units? g(x) = (x - 1)² + 1 g(x) = (x + 5)² + 1 g(x) = (x + 2)² - 2 g(x) = (x + 2)² + 3

If f(x)=2x-2 and g(x)=x+1, then f(x) = g(x) when

The function f(x)=x³-3 is one-to-one. a. Find an equation for f1, the inverse function. b. Verify that your equation is correct by showing that f(f^-1(x)) = x and f^-1(f(x))=x.

Use transformations of the graph of f(x)= ex to graph the given function. Be sure to give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm the hand-drawn graphs. h(x) = e^-x ***** Determine the transformations that are needed to go from f(x)= ex to the given graph. Select all that apply. A. shrink horizontally B. reflect about the x-axis C. stretch vertically D. reflect about the y-axis E. shift f(x) upward by 1 unit F. shift f(x) to the left by 1 unit G. stretch horizontally H. shrink vertically I. shift f(x) to the right by 1 unit J. shift f(x) downward by 1 unit

For the linear function f(x) = 7x - 4, find the range of f(x) at x = -2, 0, and 2. A) f(-2) = 10, f(0) = -4, f(2)= -18 B) f(-2) = -18, f(0) = -4, f(2)= 10 C) f(-2) = 18, f(0) = -4, f(2)= 10 D) f(-2) = -18, f(0) = 4, ƒ(2) = 10

f(x) = x³ +2 and g(x) = x - 3 Step 2 of 2: Find the formula for (f/g)(x) and simplify your answer. Then find the domain for (f/g)(x). Round your answer to two decimal places, if necessary. (f/g)/x)= Domain =

Consider the function given by f(x)=6x+5. (a) Find its average rate of change from x=1 to x=5. (b) Find its average rate of change from x=-2 to x=6. (c) The average rate of change for this function is always 6 (as you should have found in the first two parts of the problem). What type of function has a constant average rate of change? What do we call this average rate of change in this case? Search the Internet if needed.

For f(x)= a. fog X-7 x+6 a. (fog)(x) = O. A. and g(x)= b.gof b. (gof)(x) = X+2 X-3' find the following composite functions and state the domain of each. 23-6x 7x-16 What is the domain of fog? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. c. fof The domain is xx#3,x # 3x + 5 - 2x - 25 (Factor completely. Simplify your answer.) d. gog 16 7 (Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression.) B. The domain is all real numbers. (Factor completely. Simplify your answer.) ……….. -25 2 What is the domain of g of? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The domain is xx# -,x#-6 *{*** (Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression.) B. The domain is all real numbers. c. (f of)(x) = (Factor completely. Simplify your answer.)

The function f(x)=x^3/5 -1, x20 is one-to-one. Use this information to answer parts a through b. (a) f(x)= (Simplify your answer.)

The graph of the function f(x) log7 (x) is stretched vertically by a factor of 4, shifted to the left by 5 units, and shifted down by 3 units. Find the equation of the function g(x) described above. Note: If you are using log you need to type it in and use the subscript button on the keyboard. There is no log button. Provide your answer below: g(x)=

For each problem below, use either sine or cosine to draw a picture of the data presented. Then find the period, amplitude, vertical/horizontal shifts and give the equation for the function. Finally, answer the question asked at the end of each problem using the function you created. 1) The temperature in a chemical storage room must have an average temperature of 72º and cannot be off by more than 12 during any hour. At what time(s) is the temperature exactly 71º?

A real estate company balances the books for its business on the first day of each month. It hopes to sell houses every other day of the month. The average number of houses, S, the company sells each day, t, is represented by the inverse of the function S-¹ =1² +4t-5/1²-7t+6 Which equation represents the average sales each day for the real estate company?

The function f(x) = 1/4(x - 2)² + 10 , x ≥ 2 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.

The functions r and s are defined as follows. r(x) = -x+2 s(x) = 5x+1 Find the value of s (r (-4)).

f(x)=√x +9. Find (x) f-¹and its domain. A. f-¹(x) = (x - 9)²; x≥9 B. f-¹(x) = x² - 9; x≥ 9 C. f-¹(x) = (x - 9)²; x≥ 0 D. f-¹(x)=x²-9;x≥0

For f(x) =2/x-5 and g(x)=9/x find the following composite functions and state the domain of each. (a) fog (b) gof (c) fof (d) gog

Consider the following function. Correct v(x) = (x + 7)³ Step 2 of 2: Determine the domain and range of the original function. Express your answer in interval notation

For f(x) = 6x + 7 and g(x)=x², find the following composite functions and state the domain of each. (a) fog (b) gof (c) fof (d) gog (a) (fog)(x) = 6x² +7 (Simplify your answer.) Select the correct choice below and, if necessary, fill in the answer box within your choice. ***** A. 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) = 36x² +84x +49 (Simplify your answer.) Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The domain of g of is {x}. O (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 g of is all real numbers.

Solve the problem. The rational function C(x) = 140x 100-x' describes the cost, C, in millions of dollars, to inoculate x% of the population against a particular strain of the flu. Determine the difference in cost between inoculating 70% of the population and inoculating 50% of the population. (Round to the nearest tenth, if necessary.) $186.6 million $186.7 million $0.8 million 0 ≤ x < 100 $0.9 million

Watch the video that describes evaluating combinations of functions. Click here to watch the video. Let f(x)=x-3 and g(x)=x²-x. Find and simplify the expression. (f+g)(-2) (f+g)(-2)=(Simplify your answer.)

Consider the following relation. S = {(8, 7), (1, 9), (5. – 5), (9. −4)} Step 2 of 2: Find the domain and range of the inverse. Express your answer as a set of numbers.

The functions r and s are defined as follows. r(x)=2x+2 s(x)=−2x²-2 Find the value of s (r(-4)).

Graph the function. g(x)=-3x² Plot five points on the graph of the function: one point with x=0, two points with negative x-values, and two points with positive x-values. Then tap on the graph-a-function button.

Graph of the function f(x) = logi (x). You can only graph integer points, for example you cannot plot the point -1. 1/4) There is one point that can be moved above and below the z axis as needed. Do not move either point off of the graph as you will not be able to click on the point again.

The functions q and r are defined as follows. q (x) = -x r(x) = -x²+2 Find the value of r (q (5)).

The equation, d(t) = 255t + 5654 represents the tuition, d dollars, at a college for the year that is t years since 2002. Find an inverse function for this model. 0000 -255 5654 +5654 255 -5654 255 +255 5654

Find (f g)(1) for the following functions. Answer How to enter your answer (opens in new window) f(-2) = -13 and g(1) = -2 (fog)(1) =

Determine if the following function is even, odd, or neither. m=|x|/2=1

Consider the following functions. f(x) = -4x and g(x) = x − 3 Find the formula for (f + g)(x) and simplify your answer. Then find the domain for (f + g)(x). Round your answer to two decimal places, if necessary.

The functions s and t are defined as follows. s(x)=2x+1 t(x)=-2x²-2 Find the value of s (t (2)).

For f(x) =x/x-7 and g(x) = -6/x, find the following composite functions and state the domain of each. O A. 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 f o g is all real numbers. (a) fog X X-7 (a) (fog)(x) = and g(x)= (b) gof 7x+6 X (c) fof (d) gog (Simplify your answer.) Select the correct choice below and, if necessary, fill in the answer box within your choice. *****

Consider the following functions. f(x) = x² + 3 and g(x) = x^1/2 Find the formula for (f/g) (x) and simplify your answer. Find domain for (f/g) (x).

The total world population is forecast to be P(t) = 0.00078+³ -0.0715t² +0.89t + 6.04 (0 ≤ts 10) in time t, where t is measured in decades, with t= 0 corresponding to 2000 and P(t) is measured in billions. (a) When is the total world population forecast to peak? In what year? You MUST justify that your result is an optimal value. t = (Round your answer down to the nearest tenth.) The corresponding year is . (Round your answer down to the nearest year.) (b) At what number will the population peak? (Round your answer to two decimal places.) billion

The rat population in a major metropolitan city is given by the formula n(t): 58e 0.015t where t is measured in years since 2002 and n(t) is measured in millions. What was the rat population in 2002? What does the model predict the rat population was in the year 2019?

A sample of bacteria is decaying according to a half-life model. If the sample begins with 500 bacteria, and after 10 minutes there are 250 bacteria, after how many minutes will there be 20 bacteria remaining? When solving this problem, round the value of k to four decimal places and round your final answer to the nearest whole number.

Expand the function f(x) = -4 (x+5) (x - 2) (x-7)

The function f(x) is given by the set of ordered pairs. {[(8, -3), (0, 4), (1, -5), (2, -1), (-6, 10)} Which is true regarding the function? f(-3) = 8 f(3) = 5 f(8) = 0 f(-6)= 10

Given f(x)= 14/x+5 and g(x)=3√x, find the following expressions. (a) (fog)(4) (b) (gof)(2) (c) (fof)(1) (d) (gog)(0) (a) (fog)(4) =

Write the point-slope form of the equation of the line satisfying each of the following conditions. Then use the point-slope form to write the slope-intercept form of the equation in function notation. Slope = -4, passing through (-3, -7) The point-slope form of the equation is (Simplify your answer. Type an equation. Use integers or fractions for any numbers in the equation.) Let f be the name of the function. The slope-intercept form of the equation written in function notation is (Simplify your answer. Use integers or fractions for any numbers in the equation.)

What is the range of the given function? {(-2, 0), (-4, -3), (2, −9), (0, 5), (-5, 7)} {x|x = -5, -4, -2, 0, 2} {y|y = -9,-3, 0, 5, 7} {x|x = -9, -5, -4, -3, -2, 0, 2, 5, 7} {y|y = -9, -5, -4, -3, -2, 0, 2, 5, 7}

For the polynomial below, 2 is a zero. 3 g(x) = x³ + 3x² - 4x - 12 Express g (x) as a product of linear factors. g(x) =

Consider the function f(x) = cos(π/4 x) (a) Find the linearization of f(x) at the point x = 1 L(x) = (b) Use the linearization in (a) to estimate the value of cos (9π/32) cos (9π/32) =

Dan is driving on the highway. He begins the trip with 16 gallons of gas in his car. The car uses up one gallon of gas every 25 miles. Let G represent the number of gallons of gas he has left in his tank, and let D represent the total distance (in miles) he has traveled. Write an equation relating G to D, and then graph your equation using the axes below.

A piecewise function f (x) is defined by f (x) = 3x-1- 4 for x≤3 (-x² + 3x + 4) / (x² -7x+12) for x>3 Part A: Graph the piecewise function f (x) and determine the range. (5 points) Part B: Determine the asymptotes of f (x). Show all necessary calculations. (5 points) Part C: Describe the end behavior of f (x). (5 points)

The function f(x)= X+6 x-3 a. Find an equation for f(x), the inverse function. b. Verify that your equation is correct by showing that f(f(x)) = x and f¯¹(f(x)) = x. A. f¯¹(x) = a. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Simplify your answer. Use integers or fractions for any numbers in the expression.) OB. f'(x) = O c. f(x) = OD. f¹(x) = is one-to-one. For the function, 3x +6 x-1 for x 1 for x s for x 2 for all x Verify that the equation is correct f(t-¹(x)) = 10 and and f(f(x)) = f() Substitute. Simplify