Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{x-3}$$?

Accepted Answer

$$[3, \infty)$$

Question 2

A company models its profit $$P (in $$thousands of dollars) as a function of the number of units sold $$x by$$ $$P(x) = -2x^2$ + 8x + 10. $$What is the absolute maximum profit, and at how many units sold does it occur?

Accepted Answer

Maximum profit is $$18 at$$ $$x = 2$$

Question 3

Which of the following graphs passes the vertical line test and represents $$y as a $$function of $$x$$?

Accepted Answer

A straight line with positive slope

Question 4

Given the function $$f(x) = \frac{1}{x-2}$$, which of the following statements is true?

Accepted Answer

The function has a vertical asymptote at $$x = 2.$$

Question 5

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$

Question 6

A function $$f is $$said to be bounded below if:

Accepted Answer

There is a number $$b$$ such that $$b \leq f(x)$$ for all $$x in $$the domain.

Question 7

Which of the following best describes the end behavior of $$f(x) = -2x^4$ + 3x^2$ - 1 as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o -\infty$$

Question 8

Suppose $$f(x) is $$increasing on $$(-\infty, 1)$$ and decreasing on $$(1, \infty). $$What can you conclude about $$x = 1$$?

Accepted Answer

$$x = 1 is a $$local maximum

Question 9

Which of the following is the range of the function $$f(x) = \frac{1}{x}$$?

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Question 10

A function $$f is $$said to be odd if:

Accepted Answer

$$f(-x) = -f(x)$$ for all $$x in $$the domain

Question 11

Which of the following is an example of a removable discontinuity?

Accepted Answer

A hole in the graph at $$x = a$$

Question 12

If a function $$f is $$constant on the interval $$[2, 5]$$, which of the following is true for any $$x_1$$, $$x_2$$ \in [2, 5]$$?

Accepted Answer

$$f(x_1$) = f(x_2$)$$

Question 13

Which of the following best describes the symmetry of the function $$f(x) = x^4$?

Accepted Answer

Symmetric with respect to the $$y-$$axis

Question 14

A real-world application: The height $$h (in $$meters) of a ball thrown upward from a building is given by $$h(t) = -4.9t^2$ + 20t + 50. $$What is the maximum height the ball reaches?

Accepted Answer

$$h = 90$$ meters

Question 15

Which of the following statements about the function $$f(x) = \frac{x^2$-1}{x-1} is $$true?

Accepted Answer

The function has a removable discontinuity at $$x = 1.$$

Question 16

Which of the following best describes the horizontal asymptote of $$f(x) = \frac{2x}{x+1}$$?

Accepted Answer

$$y = 2$$

Question 17

If $$f(x) is $$decreasing on $$(-\infty, 0)$$ and increasing on $$(0, \infty)$$, what can you say about $$x = 0$$?

Accepted Answer

$$x = 0 is a $$local minimum

Question 18

Which of the following is the implied domain of $$f(x) = \frac{1}{x^2$-4}$$?

Accepted Answer

$$(-\infty, -2) \cup (-2, 2) \cup (2, \infty)$$

Study Guide: Functions and Their Properties in Precalculus

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