Question 1

Which of the following points is located 3 units to the right of the origin and 2 units down in the rectangular coordinate system?

Accepted Answer

$$(3, -2)$$

Question 2

Given the equation $$y = 2x + 5$$, what is the y-intercept of its graph?

Accepted Answer

$$(0, 5)$$

Question 3

Which of the following relations is a function?

Accepted Answer

$$\{(1, 2), (2, 3), (3, 4)\}$$

Question 4

If $$f(x) = x^2$ - 4$$, what is the value of $$f(-3)$$?

Accepted Answer

$$5$$

Question 5

Which of the following equations does NOT define $$y as a $$function of $$x$$?

Accepted Answer

$$x^2$$ + $$y^2 = 1$

Question 6

Given the function $$f(x) = |x|$$, on which interval is the function decreasing?

Accepted Answer

$$(-\infty, 0)$$

Question 7

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$

Question 8

What is the slope of the line passing through the points $$(2, 5)$$ and $$(6, 13)$$?

Accepted Answer

$$2$$

Question 9

Which of the following lines is perpendicular to the line $$y = -\frac{1}{3}x + 2$$?

Accepted Answer

$$y = 3x - 1$$

Question 10

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

Accepted Answer

$$9$$

Question 11

What is the standard form of the equation of a circle with center $$(3, -2)$$ and radius $$5$$?

Accepted Answer

$$(x - 3)^2$ + (y + 2)^2$ = 25$$

Question 12

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

Accepted Answer

$$[2, \infty)$$

Question 13

If $$f(x) = 3x - 4$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 4}{3}$$

Question 14

A machine produces open boxes from $$15 in by$$ $$8 in $$sheets by cutting squares of side $$x$$ from each corner. What is the volume $$V of $$the box as a function of $$x$$?

Accepted Answer

$$V(x) = x(15 - 2x)(8 - 2x)$$

Question 15

Which transformation will shift the graph of $$f(x) to $$the left by $$4$$ units?

Accepted Answer

$$f(x + 4)$$

Question 16

If $$f(x) = x^2$ and g(x) = x + 1$, what is the domain of $$\frac{f(x)}{g(x)}$$?

Accepted Answer

$$(-\infty, -1) \cup (-1, \infty)$$

Question 17

Given the line $$2x - 3y = 6$$, what is the y-intercept?

Accepted Answer

$$(0, -2)$$

Question 18

Which of the following best describes the graph of $$f(x) = \sqrt{x}$$?

Accepted Answer

It is increasing on $$[0, \infty)$$ and is neither even nor odd.

Question 19

If the distance between points $$(1, 2)$$ and $$(4, 6) is$$ $$d$$, what is $$d$$?

Accepted Answer

$$5$$

Chapter 1: Functions and Graphs – Precalculus Study Guide

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