Free Printable Unit 3 - Milestone Review

1.

Which of the relations below is a function?

a)

$(1,1),(2,1),(3,1),(4,1),(5,1)$

b)

$(0,2),(0,3),(0,4),(0,5),(0,6)$

c)

$(2,1),(2,2),(2,3),(2,4),(2,5)$

2.

The graph of a relation is shown below. Is this relation a function?

a)

Yes

b)

No

c)

Cannot be determined

3.

Is the relation depicted in the chart a function?

a)

Yes

b)

No

c)

Cannot be determined from the chart.

4.

Which graph represents a function?

a)

b)

c)

d)

5.

Give the domain and range of the relation.

a)

D: {–5, 0, 4, 6}

R: {–9, 0, 9, 13}

b)

D: {–5, 4, 6}

R: {–9, 9, 13}

c)

D: {4, 6, –5, 9, 13, –9}

R: {0}

d)

D: {–9, 0, 9, 13}

R: {–5, 0, 4, 6}

6.

Determine a relationship between the x- and y-values. Write an equation.

a)

$y=x-5$

b)

$y=-5x+1$

c)

$y=x-2$

d)

$y=-x-5$

7.

For $f\left(x\right)=-5x-3$ , find $f\left(1\right)$ .

a)

10

b)

2

c)

-13

d)

-8

8.

Using the graph, find the x and y intercepts.

a)

x-intercept: $-4$

y-intercept: $-2$

b)

x-intercept: $-4$

y-intercept: $2$

c)

x-intercept: $4$

y-intercept: $2$

d)

x-intercept: $2$

y-intercept: $-4$

9.

Give the domain and range of the relation.

a)

D: $\left\{-2,\ 4,\ 5,\ 9\right\}$

R: $\left\{0,\ 3,\ 8\right\}$

b)

D: $\left\{0,\ 3,\ 8\right\}$

R: $\left\{-2,\ 4,\ 5,\ 9\right\}$

c)

D: $-2<x<9$

R: $0<y<8$

d)

D: $2<x<9$

R: $0<y<8$

10.

Clayton has 65 stamps in her collection. To expand the collection, he is planning to buy some books of stamps that have 16 stamps each. All of the books cost the same. Clayton is not sure yet about the number of books of stamps he wants to buy, but he has enough money to buy up to 5 of them. Write a function to describe how many stamps Clayton can buy. Let x represents the number of books of stamps Clayton buys. Find a reasonable domain and range for the function.

a)

$f\left(x\right)=16x+65$

D: $\left\{0,\ 1,\ 2,\ 3,\ 4\right\}$

R: $\left\{65,\ 81,\ 97,\ 113,\ 129\right\}$

b)

$f\left(x\right)=65x+16$ D: $\left\{5\right\}$

R: $\left\{145\right\}$

c)

$f\left(x\right)=65x+16$

D: $\left\{0,\ 1,\ 2,\ 3,\ 4\right\}$

R: $\left\{81,\ 97,\ 113,\ 129,\ 145\right\}$

d)

$f\left(x\right)=16x+65$

D: $\left\{0,\ 1,\ 2,\ 3,\ 4,\ 5\right\}$

R: $\left\{65,\ 81,\ 97,\ 113,\ 129,\ 145\right\}$

11.

Find the 23^rd term in the arithmetic sequence $3,11,19,27,35,\dots$

a)

179

b)

157

c)

176

d)

187

12.

Sylvie is going on vacation. She has already driven 46 miles in one hour. Her average speed for the rest of the trip is 64 miles per hour. How far will Sylvie have driven 6 hours later?

a)

276 miles

b)

366 miles

c)

384 miles

d)

430 miles

13.

Tell whether the set of ordered pairs $\left(3,\ -5\right),\ \left(6,\ -11\right),\ \left(9,\ -17\right),\ \left(12,\ -23\right)$ satisfies a linear function. Explain.

a)

No; there is a constant change in $x$ that corresponds to a constant change in $y$ .

b)

No; there is no constant change in $x$ that corresponds to a constant change in $y$ .

c)

Yes; there is a constant change in $x$ that corresponds to a constant change in $y$ .

d)

Yes; there is no constant change in $x$ that corresponds to a constant change in $y$ .

14.

Find the slope of the line described by $3x+4y=12$

a)

$-\frac{3}{4}$

b)

$-\frac{4}{3}$

c)

$\frac{3}{4}$

d)

$\frac{4}{3}$

15.

Find the x and y intercepts of $2x-y=10$

a)

$x-intercept:\ 5$

$y-intercept:\ -9\$

b)

$x-intercept:\ 6$

$y-intercept:\ -10\$

c)

$x-intercept:\ 5$

$y-intercept:\ -10$

d)

$x-intercept:\ 6$

$y-intercept:\ -9\$

16.

Find the slope of the line.

a)

$\frac{2}{3}$

b)

$-\frac{3}{2}$

c)

$-\frac{2}{3}$

d)

$\frac{1}{3}$

17.

Tara creates a budget for her weekly expenses. The graph shows how much money is in the account at different times. Find the slope of the line. Then tell what rate the slope represents.

a)

The slope is $-50$ . The slope means that the amount of money in the account is decreasing at a rate of $50 every week.

b)

The slope is $50$ . The slope means that the amount of money in the account is increasing at a rate of $50 every week.

c)

The slope is $-0.02$ . The slope means that the amount of money in the account is decreasing at a rate of $0.02 every week.

d)

The slope is $-50$ . The slope means that the amount of money in the account is decreasing at a rate of $50 every 2 weeks.

18.

The water level of a river is 34 feet and it is receding at a rate of 0.5 foot per day. Write an equation that represents the water level, $w$ , after $d$ days. Identify the slope and y-intercept and describe their meanings. In how many days will the water level be 26 feet?

a)

$w=34d+0.5$

The slope is 34, and this is the rate at which the water level is receding. The y-intercept is 0.5, and this is the water level after 0 days. In 16 days, the water level will be 26 feet.

b)

$w=-0.5d-34$

The slope is -0.5, and this is the rate at which the water level is receding. The y-intercept is -34, and this is the water level after 0 days. In 120 days, the water level will be 26 feet.

c)

$w=34d-0.5$

The slope is 34, and this is the rate at which the water level is receding. The y-intercept is -0.5, and this is the water level after 0 days. In 120 days, the water level will be 26 feet.

d)

$w=-0.5d+34$

The slope is -0.5, and this is the rate at which the water level is receding. The y-intercept is 34, and this is the water level after 0 days. In 16 days, the water level will be 26 feet.

19.

Let $g\left(x\right)$ be the transformation, vertical translation 4 units down, of $f\left(x\right)=x-2$ . Write the rule for $g\left(x\right)$ .

a)

$g\left(x\right)=x-6$

b)

$g\left(x\right)=4x-2$

c)

$g\left(x\right)=x-2$

d)

$g\left(x\right)=x-4$

20.

Given the recursive form of the following function, determine the first 4 terms in the sequence.

$a_1=1$

$a_n=3a_{n-1}$

a)

$1,\ 3,\ 6,\ 9$

b)

$1,\ 3,\ 9,\ 27$

c)

$1,\ 2,\ 3,\ 4$

d)

$1,\ 4,\ 7,\ 10$

21.

Carlos begins with 8 baseball cards in his collection one month. Each month, he increases his collection by 2 baseball cards. The table below shows the month number and the number of cards in Carlos’ collection.

Express the function of Carlos’ baseball cards as a sequence in explicit form.

a)

$a_n=2n+6$

b)

$a_n=n+2$

c)

$a_n=n+8$

d)

$a_n=2n+8$

22.

Carlos begins with 8 baseball cards in his collection one month. Each month, he increases his collection by 2 baseball cards. The table below shows the month number and the number of cards in Carlos’ collection.

Express the function of Carlos’ baseball cards as a sequence in recursive form.

a)

$a_n=a_{n-1}+6$

b)

$a_n=2a_{n-1}+6$

c)

$a_n=a_{n-1}+2$

d)

$a_n=2a_{n-1}$

23.

John took a sample of water from the pond behind his house. On the first day, he found 1 bacteria in the sample. Each day that amount tripled. The table for one week of bacteria growth is in the sample is shown below.

Can this problem situation be described as a linear function or exponential function? How do you know?

a)

Linear, because the common ratio is 3.

b)

Linear, because the common difference is 3.

c)

Exponential, because the common ratio is 3.

d)

Exponential, because the common difference is 3.

24.

John took a sample of water from the pond behind his house. On the first day, he found 1 bacteria in the sample. Each day that amount tripled. The table for one week of bacteria growth is in the sample is shown below.

Write an explicit rule for the problem situation from above.

a)

$a_n=3^{n-1}$

b)

$a_n=3^n$

c)

$a_n=1^{n-1}$

d)

$a_n=3^{n-1}+1$

25.

John took a sample of water from the pond behind his house. On the first day, he found 1 bacteria in the sample. Each day that amount tripled. The table for one week of bacteria growth is in the sample is shown below.

Write a recursive rule for the problem situation above.

a)

$a_n=9a_{n-1}$

b)

$a_n=3a_{n-1}$

c)

$a_n=a_{n-1}+3$

d)

$a_n=a_{n-1}-3$

26.

The following two functions are graphed:

$f\left(x\right)=4x+4$

$g\left(x\right)=2^x+3$

What type of function is $f\left(x\right)$ and how do you know?

a)

Exponential, because there is an $x$ in the equation.

b)

Linear, because the rate of change is constant.

c)

Exponential, because the variable is an exponent.

d)

Linear, because there is an $x$ in the equation.

27.

The following two functions are graphed:

$f\left(x\right)=4x+4$

$g\left(x\right)=2^x+3$

Which one of the following characteristics is true for BOTH $f\left(x\right)$ and $g\left(x\right)$ ?

a)

They both have a constant rate of change.

b)

They both have y-intercept of $\left(0,\ 4\right)$ .

c)

They both are decreasing over all x-values.

d)

They both have a range of all real numbers.

28.

The following two functions are graphed:

$f\left(x\right)=4x+4$

$g\left(x\right)=2^x+3$

Which is the range of $g\left(x\right)$ ?

a)

$\left[3,\ \infty\right)$

b)

$\left(3,\ \infty\right)$

c)

All real numbers.

d)

$\left(0,\ \infty\right)$

29.

Given the following functions:

$f\left(x\right)=5x-2$

$g\left(x\right)=4^x$

Find $f\left(3\right)+g\left(2\right)$ .

a)

29

b)

3

c)

72

d)

56

30.

Given the following functions:

$f\left(x\right)=5x-2$

$g\left(x\right)=4^x$

Find $3g\left(1\right)-4f\left(2\right)$ .

a)

0

b)

44

c)

20

d)

-20

31.

Given the following functions:

$f\left(x\right)=5x-2$

$g\left(x\right)=4^x$

Find $f\left(x\right)+g\left(x\right)$ .

a)

$x-2$

b)

$5x+4^x-2$

c)

$5x+4^x$

d)

$5x-2-4^x$

32.

Sarah graphed the equation, $f\left(x\right)=3x$ on the coordinate plane below. Her partner graphed $g\left(x\right)$ on the same coordinate plane below.

Find the function equation for $g\left(x\right)$ .

a)

$g\left(x\right)=3x+4$

b)

$g\left(x\right)=3x-4$

c)

$g\left(x\right)=4\cdot3x$

d)

$g\left(x\right)=3x$

33.

Given the function $f\left(x\right)=2^x$ , find a function for $g\left(x\right)$ .

a)

$g\left(x\right)=2^x$

b)

$g\left(x\right)=2^x+4$

c)

$g\left(x\right)=2^x-4$

d)

$g\left(x\right)=4\cdot2^x$

34.

If the original function $f\left(x\right)=2^x$ , and you shifted it to the right 5, what would be the correct equation for the new, transformed function?

a)

$g\left(x\right)=2^x-5$

b)

$g\left(x\right)=-5\cdot2^x$

c)

$g\left(x\right)=2^{x-5}$

d)

$g\left(x\right)=2^{x+5}$

35.

Given the following functions:

$f\left(x\right)=3x-1$

$g\left(x\right)=2^x$

Evaluate the following: $f\left(-2\right)$ , $g\left(3\right)$ , and $f\left(m\right)$

4 lines

36.

Which mapping diagram represents a function?

a)

Mapping Diagram A

b)

Mapping Diagram B

c)

Neither

d)

Both

37.

Which of the following models an exponential function?

a)

Stew gets paid $12 per hour to cut grass

b)

A pool pumps out water at 700 gallons per minute

c)

A culture of bacteria doubles every half hour

d)

You lose $5 for every math question you miss

38.

Forevermore is a band made up of 3 of your friends. They have recorded a CD and would like to burn CDs to sell. They found two recording companies that will make a master CD and design the cover art, then make copies of the CDs. Company A charges $100 to make the master CD and design the cover art and an additional $3 per CD to make copies. Company B charges $5 per CD with no initial charge for the master CD and cover art.

Which equation represents the total cost, 𝐶, of using company A if x represents the total number of CDs produced.

a)

$C=100x+3$

b)

$C=3x+100$

c)

$C=5x+100$

d)

$C=105x$

39.

Forevermore is a band made up of 3 of your friends. They have recorded a CD and would like to burn CDs to sell. They found two recording companies that will make a master CD and design the cover art, then make copies of the CDs. Company A charges $100 to make the master CD and design the cover art and an additional $3 per CD to make copies. Company B charges $5 per CD with no initial charge for the master CD and cover art.

Give the total cost Forevermore must pay if they record 75 CDs using each company.

a)

Company A: $7503

Company B: $7875

b)

Company A: $225

Company B: $75

c)

Company A: $325

Company B: $375

d)

Company A: $400

Company B: $500

40.

Forevermore is a band made up of 3 of your friends. They have recorded a CD and would like to burn CDs to sell. They found two recording companies that will make a master CD and design the cover art, then make copies of the CDs. Company A charges $100 to make the master CD and design the cover art and an additional $3 per CD to make copies. Company B charges $5 per CD with no initial charge for the master CD and cover art.

Which below shows the correct table of values for Company A?

a)

b)

c)

41.

Forevermore is a band made up of 3 of your friends. They have recorded a CD and would like to burn CDs to sell. They found two recording companies that will make a master CD and design the cover art, then make copies of the CDs. Company A charges $100 to make the master CD and design the cover art and an additional $3 per CD to make copies. Company B charges $5 per CD with no initial charge for the master CD and cover art

Which of the following is false about the graphs the number of CDs and total cost for each company?

a)

Both graphs have a positive rate of change (slope)

b)

Company A has a y-intercept at (0, 100) and Company B has a y-intercept at (0, 0).

c)

Their intersection point is where the amount of CDs ordered costs the same for each company.

d)

The graphs do not intersect.

42.

Forevermore is a band made up of 3 of your friends. They have recorded a CD and would like to burn CDs to sell. They found two recording companies that will make a master CD and design the cover art, then make copies of the CDs. Company A charges $100 to make the master CD and design the cover art and an additional $3 per CD to make copies. Company B charges $5 per CD with no initial charge for the master CD and cover art.

If you are ordering more than 50 CDs, which company would be the cheapest?

a)

Company A

b)

Company B

43.

Which is a graph of the following function?

$f\left(x\right)=\frac{1}{2}x-2$

a)

b)

c)

d)

44.

Given the function $f\left(x\right)=\frac{1}{2}x-2$

The rate of change is ....

a)

Constant

b)

Variable

c)

-2

d)

Decreasing

45.

Given the function $f\left(x\right)=\frac{1}{2}x-2$

What happens to the end behavior on the right side of $f\left(x\right)$ ?

a)

As $x$ increases, $f\left(x\right)$ increases towards $\infty$ .

b)

As $x$ increases, $f\left(x\right)$ decreases towards $-\infty$ .

c)

There is no correlation between $x$ and $f\left(x\right)$ .

46.

Given the explicit form of the following function, determine the first 4 terms in the sequence.

$a_n=-n+3$

a)

$3,\ 2,\ 1,\ 0$

b)

$-1,\ 2,\ 5,\ 8$

c)

$2,\ 1,\ 0,\ -1$

d)

$1,\ 2,\ 3,\ 4\$

Unit 3 - Milestone Review

Total questions: 46

Worksheet time: 27mins

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