Question 1

Which of the following best describes the vertical line test for functions?

Accepted Answer

A graph is a function if every vertical line crosses the graph at most once.

Question 2

Given the function $$f(x) = \dfrac{1}{x-2}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x 
eq 2$$

Question 3

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

Accepted Answer

$$9$$

Question 4

Which of the following is NOT a characteristic of an even function?

Accepted Answer

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

Question 5

A company’s revenue is given by $$R(x) = x \cdot p$$, where $$x is $$the number of units sold and $$p is $$the price per unit. If $$p = 100 - 2x$$, what is the revenue function in terms of $$x$$?

Accepted Answer

$$R(x) = 100x - 2x^2$

Question 6

What is the difference quotient for the function $$f(x) = x^2$?

Accepted Answer

$$2x + h$$

Question 7

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$

Question 8

If a quadratic function has the form $$f(x) = ax^2$ + bx + c$$, what is the formula for the x-coordinate of its vertex?

Accepted Answer

$$x = -\dfrac{b}{2a}$$

Question 9

Given $$f(x) = \sqrt{x-3}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x \geq 3$$

Question 10

A rectangle has a length of $$x+2$$ and a width of $$x-1. $$What is the area of the rectangle in terms of $$x$$?

Accepted Answer

$$x^2 + x - 2$

Question 11

Which transformation will result in a vertical stretch of the graph of $$f(x) by a $$factor of $$a \u003e 1$$?

Accepted Answer

$$y = a f(x)$$

Question 12

If $$f(x) = |x|$$, which statement is true about its graph?

Accepted Answer

It is symmetric about the y-axis.

Question 13

What is the average rate of change of $$f(x) = 3x^2$ from x = 1$ to x = 4$?

Accepted Answer

$$15$$

Question 14

Which of the following is the correct formula for the distance between points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$\sqrt{(x_2$ - x_1$)^2$$ + ($$y_2$$ - $$y_1)^2$}$$

Question 15

If $$f(x) = x^2$ - 4x + 3$$, what are the x-intercepts of the function?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 16

Which of the following is the correct formula for the circumference of a circle with radius $$r$$?

Accepted Answer

$$2\pi r$$

Question 17

A function $$f(x) is $$defined as $$f(x) = \dfrac{2x+1}{x-3}. $$What value must be excluded from the domain?

Accepted Answer

$$x = 3$$

Question 18

If $$f(x) = x^2$ and g(x) = 2x$, what is f(g(3$$))$$?

Accepted Answer

$$36$$

Question 19

Which of the following is the correct formula for the area of a triangle with base $$b$$ and height $$h$$?

Accepted Answer

$$\dfrac{1}{2} b h$$

Question 20

If $$f(x) = x^2$ and f(a) = 16$, what is a possible value of a$?

Accepted Answer

$$4$$

Precalculus Study Notes: Functions, Graphs, and Applications

Study Guide - Practice Questions

Study Guide - Flashcards