Question 1

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

Accepted Answer

$x \geq 0$

Question 2

Given the function $y = f(x) = \frac{1}{x-1}$, which value is NOT in the domain?

Accepted Answer

$x = 1$

Question 3

A function $f$ is defined by $f(x) = 3x + 6$. What is the range of $f$?

Accepted Answer

All real numbers

Question 4

Which of the following tables represents a function?

Accepted Answer

Each input has exactly one output

Question 5

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

Accepted Answer

$10$

Question 6

A motorist travels at $70$ km/h for $2$ hours and then at $80$ km/h for $t$ hours. Which function gives the total distance $d$ traveled?

Accepted Answer

$d = 140 + 80t$

Question 7

Which of the following statements about the vertical line test is TRUE?

Accepted Answer

A graph is a function if every vertical line intersects it at most once

Question 8

Let $y = f(x) = x^2 + 2$. What are the intercepts of the function?

Accepted Answer

y-intercept: $2$, x-intercept: None

Question 9

If $f(x) = 2x + 4$, what is $f(-4)$?

Accepted Answer

$-4$

Question 10

Which of the following best describes an increasing function?

Accepted Answer

$f(x_2) > f(x_1)$ if $x_2 > x_1$

Question 11

Given $f(x) = x^2 + 2$, for which value(s) of $x$ does $f(x) = 11$?

Accepted Answer

$x = 3$ or $x = -3$

Question 12

The population of a city $P$ in millions is a function of $t$, the year, $P = f(t)$. What does $f(2005) = 12$ mean?

Accepted Answer

The population in 2005 is 12 million

Question 13

Which of the following is NOT a valid way to represent a function according to the rule of four?

Accepted Answer

As a solution to a differential equation

Question 14

Suppose $f(x) = x^2 + 4$ and $g(x) = 6x - 2$. What is $f(g(1))$?

Accepted Answer

$f(g(1)) = 38$

Question 15

A deposit is made into an interest-bearing account. If the balance $B$ after $t$ years is given by $B = f(t)$, and $f(10) = 4000$, what does this mean?

Accepted Answer

After 10 years, the balance is $4000$

Functions and Change: Foundations of Calculus (Section 1.1 Study Notes)

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