1. Chapter 1 Review Answer Key

2. Question 1 __/9 a. b. d. c. e. +1 +1 graph +1 +1 table +1 labels +1
Create a table and graph from the following situation. You are buying some new pens on Amazon. You see that each pen is going to cost you $2. When you order (even if you don’t order any pens) there is a flat $5 shipping fee.
What is the equation that models this situation?
𝑦=2𝑥+5 -or- 𝐶=2𝑛+5 +1
# of Pens
Cost in $ 5 1 7 2 9 3 11 4 13 15
Cost
+1 graph
Find an equation for the inverse.
𝑛= 𝐶−5 2
-or-
𝑦= 𝑥−5 2 +1
# of Pens
+1 table
+1 labels
Create a table and graph of the inverse of the situation.
How can we tell if two tables are inverses of each other?
Cost in $
# of Pens 5 7 1 9 2 11 3 13 4 15
# of Pens
The domain and range are flipped.
-or-
The x-variable and y-variable are flipped.
The independent and dependent variable are flipped.
The output and input are flipped. +1
+1 graph
+1 labels
+1 table
Cost

3. Question 2 __/10 They are reflections across the y=x line. a. c. d. b.
Create a table and graph from the following situation. You throw a ball off a cliff and measure how long it takes to fall and come up with the following model: 𝑑=−2 𝑡 where d is the distance from the ground in feet and t is time measured in seconds.
Find the inverse equation.
𝑡= 𝑑−50 −2
-or-
𝑦= 𝑥−50 −2 +1
Time (sec)
Distance (feet) 50 1 48 2 42 3 32 4 18 5
+1 graph
Distance
How many seconds would it take the ball to fall 20 feet?
+1 labels
+1 table +1
𝑡≈3.87𝑠𝑒𝑐
Time
Create a table and graph of the inverse of the situation.
How can we tell if two graphs are inverses of each other?
Distance (feet)
Time (sec) 50 48 1 42 2 32 3 18 4 5
Time
+1 labels
+1 graph
They are reflections across the y=x line. +1
+1 labels
+1 table
Distance

4. Question 3 __/10 𝑧= 2 8 +1 𝑧=256+1 𝑧=257 𝑧𝑒𝑏𝑟𝑎𝑠 2 𝑡 +1=3,000a. b. c. d.
Create a table and graph from the following situation. You are a biologist studying zebras in Africa. You discover that the rate of growth of zebras can be modeled by 𝑧= 2 𝑡 +1 where z is the number of zebras and t is the time in years.
How many zebras will there be after 8 years? +1 𝑧=
𝑧=256+1
𝑧=257 𝑧𝑒𝑏𝑟𝑎𝑠
Time (years)
# of Zebras 2 1 3 5 9 4 17 33
+1 labels
# of Zebras
+1 graph
+1 labels
+1 table
Time
Create a table and graph of the inverse of the situation.
About how many years will it take to get 3,000 zebras?
# of Zebras
Time (years) 2 3 1 5 9 17 4 33
Time
2 𝑡 +1=3,000
=2,049
=2,897
=2,999
About years +1
+1 labels
+1 graph
+1 labels
+1 table
# of Zebras

5. Question 4 Question 5 __/3 __/3
What are 3 other words that we use to describe the x-variable?
Domain
Input
Independent Variable +1 +1 +1
Question 5
__/3
What are 3 other words that we use to describe the y-variable?
Range
Output
Dedependent Variable +1 +1 +1

6. Question 6 Question 7 Question 8 __/2 __/2 __/1
If 𝑓 8 =15 what is 𝑓 −1 15 ? How do you know?
𝑓 −1 15 =8
Something about inverses and flipping input and output +1 +1
Question 7
__/2
If 𝑓 =3.14 what is 𝑓 − ? How do you know?
𝑓 − = 2 3
Something about inverses and flipping input and output +1 +1
Question 8
__/1
If 𝑓 𝑠 =𝑡 what is 𝑓 −1 𝑡 ?
𝑓 −1 𝑡 =𝑠 +1

7. Question 9 __/12 Steps to undo: 1) Add 6 Steps to undo:
Take the following functions and find their inverse function. Describe how you would undo the function in words and then write out the inverse equation. a. b. c. d. e. f.
𝑓 𝑥 =𝑥−6
𝑓 𝑥 = 𝑥 12
𝑓 𝑥 =4𝑥+7
Steps to undo:
1) Add 6
Steps to undo:
1) Multiply by 12
Steps to undo:
Subtract 7
Divide by 4 +1 +1 +1
𝑓 −1 𝑥 =𝑥+6 +1
𝑓 −1 𝑥 =12𝑥 +1
𝑓 −1 𝑥 = 𝑥−7 4 +1
𝑓 𝑥 = 𝑥 2 −9
𝑓 𝑥 = 2 𝑥
𝑓 𝑥 = 2 𝑥 +4
Steps to undo:
Add 9
Take the square root
Steps to undo:
Subtract 4
Take the log of base 2
Steps to undo:
Take the log of base 2 +1 +1 +1 +1 +1
𝑓 −1 𝑥 = 𝑥+9
𝑓 −1 𝑥 = log 2 𝑥 +1
𝑓 −1 𝑥 = log 2 (𝑥−4)

8. Question 10
__/4
Change the exponential form of the equation into the logarithmic form. a. b. c. d.
2 3 =8
3 4 =81
log 2 8 =3
log =4 +1 +1
10 2 =100
2 −1 = 1 2
log =2
log =−1 +1 +1

9. Total
__/56
Once you have totaled your partners score, give the review back to them.
Once you have your own review back, come to me and tell me what your score was.