Question 1

Which of the following numbers is both an integer and a rational number, but NOT a whole number?

$$	ext{A. } -4$$
$$	ext{B. } 0$$
$$	ext{C. } \sqrt{16}$$
$$	ext{D. } 2.5$$

Accepted Answer

$$-4$$

Question 2

Given the points $$A(-2, 4)$$ and $$B(0, -3)$$, what is the distance between them?

$$	ext{A. } \sqrt{53}$$
$$	ext{B. } 5$$
$$	ext{C. } 7$$
$$	ext{D. } \sqrt{29}$$

Accepted Answer

$$\sqrt{53}$$

Question 3

Which of the following intervals represents all real numbers $$x$$ such that $$-2 \u003c x \leq 5$$?

$$	ext{A. } (-2, 5]$$
$$	ext{B. } [-2, 5)$$
$$	ext{C. } (-2, 5)$$
$$	ext{D. } [-2, 5]$$

Accepted Answer

$$(-2, 5]$$

Question 4

A line passes through the points $$(1, 2)$$ and $$(3, 7). $$What is the equation of the line in slope-intercept form?

$$	ext{A. } y = 2.5x - 0.5$$
$$	ext{B. } y = 2.5x + 1$$
$$	ext{C. } y = 2.5x - 1.5$$
$$	ext{D. } y = 2.5x - 2.5$$

Accepted Answer

$$y = 2.5x - 0.5$$

Question 5

If $$f(x) = 2x + 5$$, what is the $$x-$$intercept of the function?

$$	ext{A. } (0, 5)$$
$$	ext{B. } (0, 2)$$
$$	ext{C. } (-2.5, 0)$$
$$	ext{D. } (-5/2, 0)$$

Accepted Answer

$$(-2.5, 0)$$

Question 6

A T-shirt company has a fixed cost of $$40,000$$ and a variable cost of $$3$$ per T-shirt. If the company sells T-shirts for $$10$$ each, how many T-shirts must be sold to break even?

$$	ext{A. } 4,000$$
$$	ext{B. } 5,714$$
$$	ext{C. } 6,000$$
$$	ext{D. } 7,143$$

Accepted Answer

$$5,714$$

Question 7

Suppose you have $$50,000 to $$invest in stocks and bonds. Stocks pay $$6\%$$ annually and bonds pay $$2\%$$ annually. If the annual interest income is $$1,892$$, how much was invested in stocks?

$$	ext{A. } 23,200$$
$$	ext{B. } 27,000$$
$$	ext{C. } 28,000$$
$$	ext{D. } 30,000$$

Accepted Answer

$$28,000$$

Question 8

Which of the following best describes the transformation from $$f(x) = x^2$ to g(x$$) = $$2(x-1)^2 + 3$?

$$	ext{A. }$$ Shift right 1, vertical stretch by 2, shift up 3
$$	ext{B. }$$ Shift left 1, vertical stretch by 2, shift up 3
$$	ext{C. }$$ Shift right 1, vertical compression by 2, shift up 3
$$	ext{D. }$$ Shift left 1, vertical compression by 2, shift down 3

Accepted Answer

Shift right 1, vertical stretch by 2, shift up 3

Question 9

Given $$f(x) = x^2$ - 2x + 1$$ and $$g(x) = 5 - x$$, what is $$(f \circ g)(2)$$?

$$	ext{A. } 16$$
$$	ext{B. } 4$$
$$	ext{C. } 9$$
$$	ext{D. } 25$$

Accepted Answer

$$16$$

Question 10

Which of the following is the correct interval notation for the solution to $$4x - 3 \u003e 2x - 12$$?

$$	ext{A. } (7, \infty)$$
$$	ext{B. } (-\infty, 7)$$
$$	ext{C. } (\infty, 7)$$
$$	ext{D. } (-\infty, -7)$$

Accepted Answer

$$(7, \infty)$$

Question 11

If $$f(x) = |x-4|$$, what is the domain and range of $$f$$?

$$	ext{A. } 	ext{Domain: } (-\infty, \infty), 	ext{ Range: } [0, \infty)$$
$$	ext{B. } 	ext{Domain: } [0, \infty), 	ext{ Range: } (-\infty, \infty)$$
$$	ext{C. } 	ext{Domain: } (-\infty, 4], 	ext{ Range: } [0, 4]$$
$$	ext{D. } 	ext{Domain: } [4, \infty), 	ext{ Range: } [0, \infty)$$

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$[0, \infty)$$

Question 12

Which of the following statements is TRUE about the function $$f(x) = x^3$?

$$	ext{A. } f(x)$$ is even and its graph is symmetric about the y$-axis.
$$	ext{B. } f(x)$$ is odd and its graph is symmetric about the origin.
$$	ext{C. } f(x)$$ is neither even nor odd.
$$	ext{D. } f(x)$$ is even and its graph is symmetric about the origin.

Accepted Answer

$$f(x) is $$odd and its graph is symmetric about the origin.

Question 13

A company finds it can produce 25 heaters for $$7,000$$, while producing 30 heaters costs $$8,300. $$What is the linear cost function $$C(x)$$, where $$x is $$the number of heaters?

$$	ext{A. } C(x) = 260x + 3,500$$
$$	ext{B. } C(x) = 260x + 350$$
$$	ext{C. } C(x) = 260x + 500$$
$$	ext{D. } C(x) = 260x + 5000$$

Accepted Answer

$$C(x) = 260x + 3,500$$

Question 14

Which of the following is the solution to the absolute value equation $$|x-7| = 2x + 9$$?

$$	ext{A. } x = -2$$
$$	ext{B. } x = -16$$
$$	ext{C. } x = 8$$
$$	ext{D. } x = -8$$

Accepted Answer

$$x = -8$$

Question 15

If $$f(x) = x^2$ - 2x + 7$$, what is the difference quotient $$\dfrac{f(x+h) - f(x)}{h}$$?

$$	ext{A. } 2x + h - 2$$
$$	ext{B. } 2x + h$$
$$	ext{C. } 2x + h + 7$$
$$	ext{D. } 2x - h + 7$$

Accepted Answer

$$2x + h - 2$$

Question 16

Which of the following best describes the solution set for $$|x-3| \u003c 10$$?

$$	ext{A. } (-7, 13)$$
$$	ext{B. } (3, 10)$$
$$	ext{C. } (-10, 3)$$
$$	ext{D. } (0, 7)$$

Accepted Answer

$$(-7, 13)$$

Question 17

Given the function $$f(x) = \sqrt{x-2}$$, what is the domain of $$f$$?

$$	ext{A. } (2, \infty)$$
$$	ext{B. } [2, \infty)$$
$$	ext{C. } (-\infty, 2]$$
$$	ext{D. } (-\infty, \infty)$$

Accepted Answer

$$[2, \infty)$$

Question 18

If the graph of $$y = f(x) is $$reflected across the $$x-$$axis and then shifted up by 3 units, what is the equation of the new graph?

$$	ext{A. } y = -f(x) + 3$$
$$	ext{B. } y = f(x) + 3$$
$$	ext{C. } y = -f(x) - 3$$
$$	ext{D. } y = f(-x) + 3$$

Accepted Answer

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

Precalculus Study Guide: Functions, Equations, and Graphs

Study Guide - Practice Questions

Study Guide - Flashcards