Quiz about Unit 3 - Milestone Review

Question 1

Which of the relations below is a function?

Accepted Answer

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

Answer

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

Answer

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

Question 2

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

Accepted Answer

No

Answer

Yes

Answer

Cannot be determined

Question 3

Is the relation depicted in the chart a function?

Accepted Answer

No

Answer

Yes

Answer

Cannot be determined from the chart.

Question 4

Which graph represents a function?

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Question 5

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

Accepted Answer

$$y=x-5$$

Answer

$$y=-5x+1$$

Answer

$$y=x-2$$

Answer

$$y=-x-5$$

Question 6

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

Accepted Answer

-8

Answer

10

Answer

2

Answer

-13

Question 7

Using the graph, find the x and y intercepts.

Accepted Answer

x-intercept: $$-4$$

y-intercept: $$2$$

Answer

x-intercept: $$-4$$

y-intercept: $$-2$$

Answer

x-intercept: $$4$$

y-intercept: $$2$$

Answer

x-intercept: $$2$$

y-intercept: $$-4$$

Question 8

Give the domain and range of the relation.

Accepted Answer

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

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

Answer

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

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

Answer

D: $$-2

R: $$0

Answer

D: $$2

R: $$0

Question 9

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.

Accepted Answer

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

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

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

Answer

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

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

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

Answer

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

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

Answer

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

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

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

Question 10

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

Accepted Answer

179

Answer

157

Answer

176

Answer

187

Question 11

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?

Accepted Answer

384 miles

Answer

276 miles

Answer

366 miles

Answer

430 miles

Question 12

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.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 13

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

Accepted Answer

$$-\frac{3}{4}$$

Answer

$$-\frac{4}{3}$$

Answer

$$\frac{3}{4}$$

Answer

$$\frac{4}{3}$$

Question 14

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

Accepted Answer

$$x-intercept:\ 5$$

$$y-intercept:\ -10$$

Answer

$$x-intercept:\ 5$$

$$y-intercept:\ -9\ $$

Answer

$$x-intercept:\ 6$$

$$y-intercept:\ -10\ $$

Answer

$$x-intercept:\ 6$$

$$y-intercept:\ -9\ $$

Question 15

Find the slope of the line.

Accepted Answer

$$-\frac{2}{3}$$

Answer

$$\frac{2}{3}$$

Answer

$$-\frac{3}{2}$$

Answer

$$\frac{1}{3}$$

Question 16

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.

Accepted Answer

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

Answer

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

Answer

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.

Answer

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.

Question 17

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?

Accepted Answer

$$w=-0.5d+34$$

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.

Answer

$$w=34d+0.5$$

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.

Answer

$$w=-0.5d-34$$

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.

Answer

$$w=34d-0.5$$

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.

Question 18

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 19

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

$$a_1=1$$

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 20

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?

Accepted Answer

Exponential, because the common ratio is 3.

Answer

Linear, because the common ratio is 3.

Answer

Linear, because the common difference is 3.

Answer

Exponential, because the common difference is 3.

Question 21

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.

Accepted Answer

$$a_n=3^n$$

Answer

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

Answer

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

Answer

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

Question 22

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.

Accepted Answer

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

Answer

$$a_n=9a_{n-1}$$

Answer

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

Answer

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

Question 23

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?

Accepted Answer

Linear, because the rate of change is constant.

Answer

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

Answer

Exponential, because the variable is an exponent.

Answer

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

Question 24

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 $$g\left(x\right)$$ ?

Accepted Answer

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

Answer

They both have a constant rate of change.

Answer

They both are decreasing over all x-values.

Answer

They both have a range of all real numbers.

Question 25

The following two functions are graphed:

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

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

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

Accepted Answer

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

Answer

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

Answer

All real numbers.

Answer

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

Question 26

Given the following functions:

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

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

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

Accepted Answer

29

Answer

3

Answer

72

Answer

56

Question 27

Given the following functions:

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

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

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

Accepted Answer

-20

Answer

0

Answer

44

Answer

20

Question 28

Given the following functions:

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

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

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

Accepted Answer

$$5x+4^x-2$$

Answer

$$x-2$$

Answer

$$5x+4^x$$

Answer

$$5x-2-4^x$$

Question 29

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 $$g\left(x\right)$$ .

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 30

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 31

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?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 32

Which mapping diagram represents a function?

Accepted Answer

Mapping Diagram A

Answer

Mapping Diagram B

Answer

Neither

Answer

Both

Question 33

Which of the following models an exponential function?

Accepted Answer

A culture of bacteria doubles every half hour

Answer

Stew gets paid $12 per hour to cut grass

Answer

A pool pumps out water at 700 gallons per minute

Answer

You lose $5 for every math question you miss

Question 34

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.

Accepted Answer

Company A: $325

Company B: $375

Answer

Company A: $7503

Company B: $7875

Answer

Company A: $225

Company B: $75

Answer

Company A: $400

Company B: $500

Question 35

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?

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Question 36

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?

Accepted Answer

The graphs do not intersect.

Answer

Both graphs have a positive rate of change (slope)

Answer

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

Answer

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

Question 37

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?

Accepted Answer

Company A

Answer

Company B

Question 38

Which is a graph of the following function?

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

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

Question 39

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

The rate of change is ....

Accepted Answer

Constant

Answer

Variable

Answer

-2

Answer

Decreasing

Question 40

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

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

Accepted Answer

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

Answer

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

Answer

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

Question 41

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

$$a_n=-n+3$$

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Unit 3 - Milestone Review

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