Question 1

Which of the following is the vertex form of a quadratic function?

Accepted Answer

$$y = a(x-h)^2$ + k$$

Question 2

Given the quadratic function $$y = -2x^2$ + 8x + 3$$, what is the vertex of the parabola?

Accepted Answer

$$(2, 11)$$

Question 3

A company’s revenue is given by $$R(x) = -x^2$ + 40x$$ and its cost by $$C(x) = 8x + 192. $$What is the maximum profit the company can achieve?

Accepted Answer

$$208$$

Question 4

Which transformation results in a vertical stretch of the graph of $$y = f(x) by a $$factor of $$c \u003e 1$$?

Accepted Answer

$$y = cf(x)$$

Question 5

If $$f(x) = x^2$, which equation represents a reflection about the y-axis?

Accepted Answer

$$y = f(-x)$$

Question 6

Which of the following best describes the end behavior of the polynomial $$f(x) = -3x^5$ + 2x^3$ - x + 7 as$$ $$x 	o \infty$$?

Accepted Answer

The graph falls to the right and rises to the left.

Question 7

A rational function is defined as $$f(x) = \frac{p(x)}{q(x)}. $$Which value of $$x$$ will create a vertical asymptote?

Accepted Answer

Any value that makes $$q(x) = 0$$ but not $$p(x) = 0$$

Question 8

Which of the following is the correct domain for the exponential function $$f(x) = 2^x$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 9

Solve for $$x$$: $$e^x = \frac{1}{e^4$}$$

Accepted Answer

$$x = -4$$

Question 10

Which of the following is the correct logarithmic form of the equation $$2^5 = 32$?

Accepted Answer

$$\log_2$ 32 = 5$$

Question 11

If $$f(x) = x^3$ - 2x^2$ + x - 5$$, what is the degree of the polynomial and how many turning points can its graph have at most?

Accepted Answer

Degree 3, at most 2 turning points

Question 12

Which of the following transformations shifts the graph of $$y = f(x)$$ three units to the right?

Accepted Answer

$$y = f(x - 3)$$

Question 13

Given the function $$f(x) = \log_{10} x$$, what is the value of $$x$$ when $$f(x) = 2$$?

Accepted Answer

$$x = 100$$

Question 14

A business invests $$5000$$ dollars at an annual interest rate $$r$$, compounded annually, and the investment grows to $$6100 in$$ $$5$$ years. Which equation should be used to solve for $$r$$?

Accepted Answer

$$6100 = 5000(1 + r)^5$

Question 15

Which of the following is the correct change of base formula for $$\log_2$ 7$$?

Accepted Answer

$$\log_2$ 7 = \frac{\log 7}{\log 2}$$

Question 16

Which of the following best describes the range of the exponential function $$f(x) = 3^x$$?

Accepted Answer

$$(0, \infty)$$

Question 17

If $$f(x) = x^2$, which transformation results in a vertical shift 4 units downward?

Accepted Answer

$$y = f(x) - 4$$

Question 18

Which of the following is NOT a property of polynomial functions?

Accepted Answer

A polynomial of degree $$n$$ can have at most $$n x-$$intercepts.

Question 19

Which of the following equations represents a horizontal compression of $$y = f(x) by a $$factor of $$c \u003e 1$$?

Accepted Answer

$$y = f(cx)$$

Nonlinear Functions and Their Transformations in Business Calculus

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