Q: Which of the following is the graph of the function $f(x) = x^3 - 3x$?

A cubic curve with two turning points, passing through the origin

Q: Which of the following best describes the graph of $f(x) = \lfloor x \rfloor$ (the greatest integer function)?

A step function with jumps at every integer value of $x$

Q: Which of the following best describes the transformation of the graph of $y = x^2$ to $y = (x-3)^2 + 2$?

Shift right by 3 units and up by 2 units

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

The function is undefined at $x = 0$

Question 1

Which of the following equations represents the graph of a semicircle of radius 2 centered at the origin in the $xy$-plane?

Accepted Answer

$y = \sqrt{4 - x^2}$

Question 2

A function $f(x)$ is defined as $f(x) = \sqrt{x}$. Which of the following best describes its domain?

Accepted Answer

$x \geq 0$

Question 3

Which of the following graphs represents the function $f(x) = |x|$?

Accepted Answer

A 'V' shaped graph opening upwards with vertex at the origin

Question 4

Given the piecewise function $f(x) = \begin{cases} 1, & x \geq 0 \ -1, & x < 0 \end{cases}$, what is the range of $f(x)$?

Accepted Answer

$\{-1, 1\}$

Question 5

Which of the following equations represents a parabola that opens downward?

Accepted Answer

$y = -x^2$

Question 6

A real-world scenario: The height $h$ (in meters) of a ball thrown upward from the ground is given by $h(t) = -4.9t^2 + 20t$, where $t$ is time in seconds. What is the maximum height reached by the ball?

Accepted Answer

$20.41$ meters

Question 7

Which of the following is the graph of the function $f(x) = x^3 - 3x$?

Accepted Answer

A cubic curve with two turning points, passing through the origin

Question 8

Given the function $f(x) = \sqrt{9 - x^2}$, what is the range of $f(x)$?

Accepted Answer

$[0, 3]$

Question 9

Which of the following best describes the graph of $f(x) = \lfloor x \rfloor$ (the greatest integer function)?

Accepted Answer

A step function with jumps at every integer value of $x$

Question 10

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

Accepted Answer

$9$

Question 11

Which of the following is the equation of a line passing through the points $(1,2)$ and $(3,6)$?

Accepted Answer

$y = 2x$

Question 12

A function $f$ is even if $f(-x) = f(x)$ for all $x$ in its domain. Which of the following functions is even?

Accepted Answer

$f(x) = x^2$

Question 13

Which of the following best describes the transformation of the graph of $y = x^2$ to $y = (x-3)^2 + 2$?

Accepted Answer

Shift right by 3 units and up by 2 units

Question 14

Which of the following is the solution set for $|x - 2| = 5$?

Accepted Answer

$\{7, -3\}$

Question 15

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

Accepted Answer

The function is undefined at $x = 0$

Question 16

Which of the following graphs represents a function that is not one-to-one?

Accepted Answer

A parabola opening upwards

Question 17

If $f(x) = 2x + 1$ and $g(x) = x^2$, what is $f(g(3))$?

Accepted Answer

$19$

Question 18

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

Accepted Answer

$f(x) 	o -\infty$

Question 19

A piecewise function is defined as $f(x) = \begin{cases} x+2, & x < 0 \ 2x-1, & x \geq 0 \end{cases}$. What is $f(-3) + f(2)$?

Accepted Answer

$2$

Fundamental Graphs and Properties of Precalculus Functions

Study Guide - Practice Questions

Study Guide - Flashcards