Question 1

Which of the following points is located in Quadrant III of the rectangular coordinate system?

Accepted Answer

$$(-4, -5)$$

Question 2

Given the equation $$y = 4 - x$$, what is the $$y-$$intercept of its graph?

Accepted Answer

$$(0, 4)$$

Question 3

A company’s total cost $$C(x) to $$produce $$x$$ bikes is given by $$C(x) = 100{,}000 + 150x. $$What does $$C(100)$$ represent?

Accepted Answer

The total cost to produce 100 bikes

Question 4

Which of the following relations is NOT a function?

Accepted Answer

$$\{(6, 1), (8, 3), (6, -2), (9, 1)\}$$

Question 5

Given $$f(x) = x^2$ - 2x + 7$$, evaluate $$f(-5).$$

Accepted Answer

$$52$$

Question 6

Which equation represents a vertical line?

Accepted Answer

$$x = 2$$

Question 7

The graph of $$y = |x + 1| is $$obtained from $$y = |x| by $$which transformation?

Accepted Answer

Shift left by 1 unit

Question 8

If $$f(x) = x^2$ and g(x$$) = $$x^2 - 2$, how is the graph of g$ related to the graph of f$?

Accepted Answer

It is shifted downward by 2 units

Question 9

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

Accepted Answer

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

Question 10

Given $$f(x) = 6x + 1$$, find and simplify the difference quotient $$\frac{f(x+h) - f(x)}{h}.$$

Accepted Answer

$$6$$

Question 11

Which of the following best describes the slope of the line passing through the points $$(2, -1)$$ and $$(2, -5)$$?

Accepted Answer

Undefined

Question 12

Given $$f(x) = x^3$, what is the average rate of change from x_1$ = -2 to$$ $$x_2 = 0$?

Accepted Answer

$$4$$

Question 13

Which of the following functions is even?

Accepted Answer

$$f(x) = 5x^6$ - 3x^2$ - 2$$

Question 14

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

Accepted Answer

$$(x + 3)^2$ + (y - 5)^2$ = 9$$

Question 15

Given $$f(x) = x^2$ + 3x - 17$$, what is the domain of $$f$$?

Accepted Answer

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

Question 16

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

Accepted Answer

$$x^2 + x - 6$

Question 17

Given $$f(x) = 2x + 7$$, find $$f^{-1}(x$$)$$, the inverse function.

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 7}{2}$$

Question 18

Which transformation results in the graph of $$y = f(x) + 3$$ from $$y = f(x)$$?

Accepted Answer

Shift up by 3 units

Question 19

Given $$f(x) = |x|$$, which equation represents a vertical stretch by a factor of 2?

Accepted Answer

$$y = 2|x|$$

Question 20

Given $$f(x) = x^2$ and g(x) = x - 3$, what is (f$$ \circ g)(x)$$?

Accepted Answer

$$(f \circ g)(x) = (x - 3)^2$

Graphs, Functions, and the Rectangular Coordinate System: Precalculus Study Guide

Study Guide - Practice Questions