Q: If the average rate of change of $g(x)$ on $[2,5]$ is $4$, and $g(2) = 3$, what is $g(5)$?

$g(5) = g(2) + 4 \times (5-2) = 3 + 12 = 15$

Q: A man has 120 coins, all dimes ($d$) and nickels ($n$). The coins are worth $9.15. Which system of equations models this situation?

$\begin{cases} d + n = 120 \\ 0.10d + 0.05n = 9.15 \end{cases}$

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

$f(g(3)) = 2 \times 9 + 1 = 19$

Q: If $f(x) = 2x + 3$ and $g(x) = x - 1$, what is $(f + g)(4)$?

$(f + g)(4) = f(4) + g(4) = (2 \times 4 + 3) + (4 - 1) = 8 + 3 + 3 = 14$

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

$f(g(2)) = (2 \times 2 + 1)^2 = (5)^2 = 25$

Question 1

Which of the following best describes the domain of the function $f(x) = \dfrac{1}{x-5}$?

Accepted Answer

$(-\infty, 5) \cup (5, \infty)$

Question 2

Given the table below, which type of function best models the data?

Distance (miles): 1.5, 4, 6, 8, 12
Fare ( 2): 5.30, 11.30, 15.10, 18.90, 26.50

Accepted Answer

Linear function

Question 3

Suppose $f(x) = 3x + 2$ and $g(x) = x^2 - 1$. What is $(f \circ g)(2)$?

Accepted Answer

$f(g(2)) = 3(2^2 - 1) + 2 = 3(3) + 2 = 11$

Question 4

A company manufactures bikes at a cost of $60 per bike, with a fixed monthly cost of $1,585. The bikes are sold for $85 each. Which equation represents the monthly break-even point?

Accepted Answer

$60x + 1585 = 85x$

Question 5

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

Accepted Answer

$[3, \infty)$

Question 6

If the average rate of change of $g(x)$ on $[2,5]$ is $4$, and $g(2) = 3$, what is $g(5)$?

Accepted Answer

$g(5) = g(2) + 4 	imes (5-2) = 3 + 12 = 15$

Question 7

A man has 120 coins, all dimes ($d$) and nickels ($n$). The coins are worth $9.15. Which system of equations models this situation?

Accepted Answer

$\begin{cases} d + n = 120 \ 0.10d + 0.05n = 9.15 \end{cases}$

Question 8

Which of the following is the equation of the line passing through the points $(1,3)$ and $(3,11)$?

Accepted Answer

$y = 4x - 1$

Question 9

If $f(x) = 2x^2 + 3x - 4$, what is $f(-2)$?

Accepted Answer

$2(-2)^2 + 3(-2) - 4 = 8 - 6 - 4 = -2$

Question 10

A rideshare service charges a base fare plus a cost per mile. If the fare for 4 miles is $11.30 and for 8 miles is $18.90, what is the cost per mile?

Accepted Answer

$\dfrac{18.90 - 11.30}{8 - 4} = \dfrac{7.60}{4} = 1.90$

Question 11

Which of the following best describes the range of the function $f(x) = x^2 - 4$?

Accepted Answer

$[-4, \infty)$

Question 12

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

Accepted Answer

$f(g(3)) = 2 	imes 9 + 1 = 19$

Question 13

Which of the following is a function whose domain is all real numbers except $x = 7$?

Accepted Answer

$f(x) = \dfrac{1}{x-7}$

Question 14

A classroom has tables that seat two students per table. Three extra tables are needed for the instructor and computer equipment. If the number of tables is given by $T(n) = \dfrac{n}{2} + 3$, where $n$ is the number of students, what is the maximum number of students who can attend a class in a room with 17 tables?

Accepted Answer

$n = 2 	imes (17 - 3) = 28$

Question 15

Which of the following best describes the average rate of change of a linear function?

Accepted Answer

It is constant for all intervals.

Question 16

If $f(x) = 2x + 3$ and $g(x) = x - 1$, what is $(f + g)(4)$?

Accepted Answer

$(f + g)(4) = f(4) + g(4) = (2 	imes 4 + 3) + (4 - 1) = 8 + 3 + 3 = 14$

Question 17

Which of the following tables represents an exponential function?

Accepted Answer

x: 0, 1, 2, 3; y: 2, 6, 18, 54

Question 18

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

Accepted Answer

$f(g(2)) = (2 	imes 2 + 1)^2 = (5)^2 = 25$

Question 19

Which of the following best describes the solution to the system:
$\begin{cases} 2x + y = 10 \ x - y = 4 \end{cases}$?

Accepted Answer

$x = 6, y = -2$

Unit 1 Review: Reasoning with Functions and Linear Models

Study Guide - Practice Questions

Study Guide - Flashcards