Question 1

Which of the following statements best describes the purpose of calculus?

Accepted Answer

Calculus deals with finding rates of change (derivatives) and areas, lengths, and volumes (integrals).

Question 2

Given the function $f(x) = |x|$, which of the following is true about its graph?

Accepted Answer

It is a V-shaped graph symmetric about the y-axis.

Question 3

Which of the following sets includes all rational numbers?

Accepted Answer

$\mathbb{Q}$ (rational numbers)

Question 4

A function $f(x)$ is called even if:

Accepted Answer

$f(x) = f(-x)$

Question 5

Which of the following is the correct difference quotient for the function $f(x)$?

Accepted Answer

$\dfrac{f(x+h) - f(x)}{h}$

Question 6

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

Accepted Answer

$x \geq 0$

Question 7

Which of the following intervals represents the solution to the compound inequality $x < -3$ or $x > 2$?

Accepted Answer

$(-\infty, -3) \cup (2, \infty)$

Question 8

A vertical line has which of the following equations?

Accepted Answer

$x = a$

Question 9

Which function is an example of an odd power function?

Accepted Answer

$f(x) = x^3$

Question 10

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

Accepted Answer

$(x + 1)^2$

Question 11

Which of the following is NOT a transcendental function?

Accepted Answer

$f(x) = x^2$

Question 12

The vertical line test is used to determine if a graph represents a function. Which statement is correct?

Accepted Answer

If a vertical line intersects the graph only once everywhere, it is a function.

Question 13

Which of the following describes an increasing function?

Accepted Answer

A function that never decreases and may stop for a while.

Question 14

Given $f(x) = x^2$ and $g(x) = x^3$, which of the following is $f(x) + g(x)$?

Accepted Answer

$x^2 + x^3$

Question 15

Which of the following is the correct point-slope form of a line passing through $(x_1, y_1)$ with slope $m$?

Accepted Answer

$y = m(x - x_1) + y_1$

Question 16

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

Accepted Answer

$x \geq 0$

Question 17

Which of the following is the correct intercept form of a line with x-intercept $a$ and y-intercept $b$?

Accepted Answer

$\dfrac{x}{a} + \dfrac{y}{b} = 1$

Question 18

Which of the following is the correct expression for the absolute value function?

Accepted Answer

$f(x) = |x|$

Question 19

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

Accepted Answer

$(x^3)^2$

Foundations of Calculus: Functions, Domains, and Graphs

Study Guide - Practice Questions