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

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