Functions Questions and Answers

Which of the following is a power function? Select all correct answers. Select all that apply: ☐ f(x) = 6 · 16ª □ f(x) = 4√x f(x) = 10.32 Of(x) = 5.15* f(x) = -183 X FE

What is the leading coefficient of a third degree polynomial function that has an output of 1,272 when x = of -6, 7i, and -7i? Provide your answer below: = 2, and has zeros

Evaluate the function. 10) f(a)=a²; Find f(-4) A) 64 C) 1 B) 100 D) 16

Given that the polynomial f(x) has degree 7, 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 least 8 turning points. The graph of f(x) has at most 7 turning points. The graph of f(x) has at least 7 turning points. The graph of f(x) has at least 6 turning points. The graph of f(x) has at most 8 turning points. The graph of f(x) has at most 6 turning points.

As a approaches negative infinity, for which of the following functions does f(x) approach negative infinity? Select all that apply. Select all that apply: f(x) = -5x8 f(x) = 7x² f(x) = x³ + 18 f(x) = 2x5 - 3x +26 f(x) = 8x² + 9x - 45 ƒ(x) = −5x³ + 14x²-8x + 76

g(x) = 4x f(x)=-3x+3 Find (g. f)(x) A) 2x² - 11x + 12 B) -12x² + 12x C) -12x² - 12x D)-x+x+4x-4

Consider the following function. f(x) = -3/10 |x| Identify the general shape of the graph of this function.

Find the real zeros of f. Use the real zeros to factor f. f(x)= x³ +6x²-9x-14 The real zero(s) of f is/are (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers. Use the real zero(s) to factor f. f(x) = (Factor completely. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression)

Write a quadratic equation having the given number as a solution. 9, only solution (Hint: It must be a repeated solution.)

Suppose that the number of employees in a new company is expected to grow, with the number of employees modeled by N = 1000(0.02)0.7¹, where t is the number of years after the company was formed. a) How many employees did the company have when it started? N= employees (Do not round until the final answer. Then round to the nearest integer as needed.)

The president of a company predicts that sales will increase rapidly after a new product is brought to the market and that the number of units sold monthly can be modeled by N = 50,000(0.4)0.2¹, where t represents the number of months after the product is introduced. a) How many units will be sold by the end of the fourth month? N = units (Do not round until the final answer. Then round to the nearest integer as needed.)

Graph f(x) = 4x-3 + 2 using transformations by first graphing the basic exponential function (parent function), then the progression of transformations (in the correct order). State the domain, range, and horizontal asymptote.

Choose the term from the box that best completes each statement. end behavior symmetric about a line even function power function 1. A function is 2. The. and as x approaches negative infinity. 3. A(n) 4. A function is. if the line divides the graph into two identical parts. of a graph of a function is the behavior of the graph as x approaches infinity 5. A(n). 6. A(n) symmetric about a point odd function has a graph symmetric about the origin, thus f(x) = -f(-x). central point but in the opposite direction. if each point on the graph has a point the same distance from the has a graph symmetric about the y-axis, thus f(x) = f(-x). is a function of the form P(x) = ax", where n is a non-negative integer.

Solve the inequality. Express your answer using set notation or interval notation. Graph the solution set. 4-3x≤ - 14 Choose the correct answer below that is the solution set to the inequality. OA. {x|x2 -6} or [-6,00) B. {xx≥ -18) or [-18,00) OC. (xlx ≥ 6) or [6,00) OD. (xx≤6) or (6,00)

Find all complex solutions of 2x²-x+6=0. (If there is more than one solution, separate them with commas.) x = X 0.0.. 0/6 ?

Consider the function f(x) = x² + 3x - 3: (a) Evaluate f(2) (b) Evaluate f(-2) (c) Find all x such that f(x) = 7 (d) Find all x such that f(x) = 9 (For part (d) express the answers exactly and round to four places.)

Rational functions vand w both have a point of discontinuity at x = 7. Which equation could represent function w? A MX)= V(X-7) B. M(x) = V(x+7) C. M(x)=V(x-7)+7 D. M(x) = V(X) + 7

The square of y varies directly as the cube of x. When x = 4, y = 2. Which equation can be used to find other combinations of x and y?

Select the correct answer. The domain of rational function g is the same as the domain of rational function f. Both fand g have a single x-intercept at x = -10. Which equation could represent function g? A (x)=10x) B. g(x)=x+10) C. g(x)=f(x) + 10 D. g(x)=f(x) - 10

Select the correct answer. Consider these functions: f(x) = -2x - 1 g(x) = -1/2 x + 1/2 Which statements, if any, are true about these functions? 1. The function f(g(x)) = x for all real x. II. The function g(x)) = x for all real x. III. Functions fand g are inverse functions. A. I only B. II only C. I, II, and III D. None of the statements are true.

A solid object is dropped into a pond with a temperature of 20 degrees Celsius. The function f(t) = Ce-kt) + 20 represents the situation, where t is time in minutes, C is a constant, and k = 0.0399. After 4 minutes the object has a temperature of 35 degrees Celsius. What was the initial temperature of the object? Round your answer to the nearest tenth, and do not include units.

Consider this function: f(x)=√x - 4 To determine the inverse of the given function, change fx) to y, switch and solve for The resulting function can be written as f(x) = x² + where x≥

The number N of bacteria after t hours is N(t) = A 2. Initially there are 150 bacteria. How many are there after 7 hours? N(7) = =

In 2012, the population of a city was 6.47 million. The exponential growth rate was 1.89% per year. a) Find the exponential growth function. b) Estimate the population of the city in 2018. c) When will the population of the city be 9 million? d) Find the doubling time. ***** Next q a) The exponential growth function is P(t)=, where t is in terms of the number of years since 2012 and P(t) is the population in millions. (Type exponential notation with positive exponents. Do not simplify. Use integers or decimals for any numbers in the equation.)

Recall that one method for treating this type of limit is by taking the natural logarithm. If we let y = [f(x)]⁹(x), then In(y) = g(x) In (f(x)). Applying this method gives the following result. y = (1 - 5x)1/x In(y) = ¹/in(1-([ × )x) We note that this leads to an indeterminate product on the right side, which is of type

The domain of the function in interval notation is (-∞, 3) U (3,∞) (b) Simplify the rational expression defining the function. f(x)=x^2+x-12/x-3 simplifies to f(x) = ___where x≠___

t) Next MA To get a better look at the graph, you can click on it. The curve above is the graph of a sinusoidal function. It goes through the point (4,0). Find a sinusoidal function that matches the given graph. If needed, you can enter TT= 3.1416... as 'pi' in your answer, otherwise use at least 3 decimal digits. f(x) =

Evaluate the function. f(x) =−x² + 3x + 13 Find f(-10)

The exponential function D(t) = 347(1.024)t gives the number of bachelor's degrees, in thou- sands, earned in the United States t years after 1970 (Sources: National Center for Educational Statistics; U.S. Department of Education). Find the number of bachelor's degrees earned in 1985, in 2000, and in 2014. Then estimate the number of bachelor's degrees that will be earned in 2020. Round to the nearest thousand degrees.

Suppose that the polynomial function fis defined as follows. f(x)=7(x-13)³(x+11) (x-11) (x+8) List each zero off according to its multiplicity in the categories below. If there is more than one answer for a multiplicity, separate them with commas. If there is no answer, click on "None." Zero(s) of multiplicity one: Zero(s) of multiplicity two: Zero(s) of multiplicity three:

. Salvage Value. A landscape company purchased a backhoe for $56,395. The value of the backhoe each year is 90% of the value of the preceding year. After t years, its value, in dollars, is given by the exponen- tial function V(t) = 56,395 (0.9)'. I a) Graph the function. b) Find the value of the backhoe after 0, 1, 3, 6, and 10 years. Round to the nearest dollar.

Macy is studying graphs of functions y = f(x). Each set in the table contains some points on a particular graph. Decide whether each set of points MIGHT BE on the graph of a function or CANNOT BE on the graph of a function. Yes These points MIGHT BE Set of points {(-3,-3), (0, 0), (3,3), (6,6), (9,9)} {(–3,0), (0,0), (3,0), (0,6), (9,0)} {(0, -3), (0,0), (0,3), (0,6), (0,9)} {(-3,0), (0,0), (3,0), (6,0), (9,0)} No These points CANNOT BE O

An object moves in simple harmonic motion with period 8 minutes and amplitude 12 m. At time t=0 minutes, its displacement d from rest is - 12 m, and initially it moves in a positive direction. Give the equation modeling the displacement d as a function of time t.

Fill in the blanks. The exponential function given by f(x) = e is called the ---Select- base and its approximate value is ---Select--- function, and the base e is called the (Round your answer to five decimal places).

Describe the end behavior of the polynomial below using limit notation f(x) = (2x² - 4x³ + 1)(x²-17)

Your car radiator can hold 20 liters of fluid. Many automotive stores sell jugs of pure antifreeze, but some also sell jugs of antifreeze that have been premixed with water. Suppose you buy a jug of 30% antifreeze mixture as well as a jug of pure antifreeze. How many liters of each jug must you use to make enough of a 89.5% mixture to fill your radiator?

For each pair of functions f and g below, find f(g(x)) and g (f(x)). Then, determine whether fand g are inverses of each other. Simplify your answers as much as possible. (Assume that your expressions are defined for all .x in the domain of the composition. You do not have to indicate the domain.) (a) f(x) = 3x g(x) = x/3 f(g(x)) = g(f(x)) = f and g are inverses of each other f and g are not inverses of each other (b) f(x) = 2x + 5 g(x) =x+5/2 f(g(x)) = 0 g(f(x)) = 0 f and g are inverses of each other f and g are not inverses of each other

Let y = 2(x-4)^2-8. Part A: Is the given relation a function? Is it one-to-one? Explain completely. If it is not one-to-one, determine a possible restriction on the domain such that the relation is one- to-one.

Find the domain and the range of the given relation. {(0,-5), (-4,1), (9,5), (5,9)} The domain is. (Use a comma to separate answers as needed.) The range is. (Use a comma to separate answers as needed.)

Describe the transformation(s) of g (z) = (x+4)²-3 from its parent function of f(x) = x² left 4, up 3 left 4 down 3 right 4 up 3 right 4, down 3 up 4, right 3 Oup 4, down 3

Describe the transformation of f(x) = 10x which is given by g(x) = 103x. A) g(x) is shrunk horizontally by a factor of 1/3 compared to f(x). B) g(x) is stretched horizontally by a factor of 3 compared to f(x). C) g(x) is shrunk vertically by a factor of 1/3 compared to f(x). D) g(x) is stretched vertically by a factor of 3 compared to f(x).

Suppose the function is defined, for all real numbers, as follows. -5x+3 if x≤2 f(x)= { } x-4 if x>2 Graph the function f. Then determine whether or not the function is continuous. Is the function continuous? Yes No

Write the function f(x) = |-4x + 36| as a piecewise-defined function. A. f(x) =4x - 36, if x ≤ 9 -4x + 36, if x >9 B. f(x) = -4x + 36, if x < 9 4x - 36, if x > 9 C. f(x) =4x − 36, if x ≤ -9 -4x + 36, if x>-9 D. f(x) =-4x + 36, if x < −9 4x-36, if x > -9

Does the function f(x) = 5e0.25x represent exponential growth, decay, or neither? A) Exponential decay B) Exponential growth C) Neither D) Impossible to determine with the information given.

Ana is bowling. She pays $4 per game and $7 to rent shoes. After three games, each additional game is free. Is the total cost to bowl a function of the number of games played? Use a table or graph to help explain your answer.

(a) Use transformations of the graph of y=e* to graph the given function n (x)=-e*+1.

According to the Mini-Lesson, which of the following are TRUE regarding f(x) = a(b)? Check all that apply. Assume a > 0. The Horizontal Asymptote is the line y = 0. The Domain of the exponential functions is All Real Numbers. The Range of the exponential functions is All Real Numbers. The Domain of the exponential functions is > 0. The Range of the exponential functions is f(x) > 0. The Horizontal Asymptote is the line a The Horizontal Asymptote is the point (0, a).

Consider the following relation. y = x + 1 Find the domain and range of the Inverse. Express your answer in Interval notation.

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. g(x) = log (x-4) Determine the transformations that are needed to go from f(x) = log x to the given graph. Select all that apply. A. shift 4 units upward B. reflect about the y-axis C. shrink vertically D. stretch horizontally E. shift 4 units to the right F. reflect about the x-axis G. shrink horizontally H. stretch vertically 1. shift 4 units to the left J. shift 4 units downward

Let A = f(r) be the area of a circle with radius r and r = h(t) be the radius of the circle at time t. Which of the following statements correctly provides a practical interpretation of the composite function f(h(t)) ? Select all that apply if more than one is appropriate. A. The area of the circle which at time t has radius h(t) . B. The length of the radius of a circle with area A = f(r) at time t. C. The area of the circle at time t. D. The length of the radius at time t. E. At what time t the radius will be r = h(t). F. At what time t the area will be A = f(r). G. None of the above