Algebra 1
Semester 1 Review Packet
Name ___________________________________
Do your work on your own sheet of paper.
Functions Part 1
1. Use the correct function rule to solve each problem. SHOW your work
𝒇(𝒙) = 𝟓𝒙 + 𝟕
𝒈(𝒙) = 𝟐𝒙 − 𝟓
1. 𝑔(𝑥) = −20
2. 𝑔(−4) =
3. 𝑓(𝑥) = 32
4. 𝑓(3.2) =
5. Find the range of the function 𝑓(𝑥) = −4𝑥 + 3 with a domain of {−1, 0, 1, 2, 3]
6. Tell whether the following situations are DISCRETE or CONTINUOUS. You must explain how you know.
a)
The car is currently going 60 mph; over the course of 1 mile. The car slowed to 15 mph.
b) Jaquelyn earns $12 for every lawn that she mows. Write the function rule to represent the total amount of money
she makes mowing lawns
7. Which of the following tables is a function? Circle the correct answer.
x
y
x
y
-2
2
-2
5
3
2
3
8
6
12
8
16
8
-2
9
4
8. Draw a graph on a relationship that is not a function.
9. a Bob’s summer job for the city is counting the cars that go through the intersection of Colby and Hewitt Avenues.
He found an equation that would model the number of cars per day
𝐶 = 2560𝑑 + 450 ( C: total number of cars, d: number of days.
If he was to graph his data should it be a continuous or discrete graph and why? ( 3pt)
b. Which of the following would be a reasonable range for this function given one month?( 3pt)
i) Between 0 and 450 ii) Between 0 and 70,0000 iii) Between 450 to infinity vi) Between 450 to 77,250
10. Represent the relationship using words, a table, an equation and a graph.
Graph
Table
x
Description/Story:
Should this graph be continuous or discrete? Why??
Function Rule
y
Functions Part 2
For questions #1 – 12, circle the letter of the graph or graphs that the statement applies to. THERE MAY BE MORE THAN
ONE GRAPH circled for a question. **1 point per question (all or nothing)
2. Range: 𝑦 > 1
1. Domain: x > 1
A
B
C
None
5. End Behavior:
As X increases, Y
increases
A
B
C
B
C
B
C
None
6. End Behavior:
As X increases, Y
decreases
None
9. The graph has a
minimum point.
A
A
3. Domain: −∞ ≤ 𝑥 ≤ ∞
A
B
C
A
B
C
None
None
a
2. Find the following key features of the graph below. (3 pts)
Domain: _______________
Range: ________________
Minimum: ___________
Maximum: ___________
Y-intercept: _________
X-intercept: _________
End Behavior:
As X decreases, Y _________________________
As X increases, Y ________________________
B
C
None
7. End Behavior:
As X increases, Y
approaches 1
10. The y-intercept is at
(0,2)
None
A
A
B
C
B
b
C
A
B
C
None
8. The graph has a
maximum point.
None
11. The y-intercept is at
(0, -2).
A
4. Range: 𝑦 ≥ 3
None
A a B
C
None
12. The x-intercept is at
(0, 2)
A
B
C
None
c
3. For each question, MARK the correct column and then explain your reasoning.
Similar
Different Explanation
Domain
Range
X-intercept(s)
Y-intercept(s)
Maximum
Minimum
End Behavior
4. Types of Functions: You will need to be able to figure out if a table, graph or equation is linear, quadratic or
exponential
A.
B.
C.
E.
D.
x
y
-2
-23
-1
2
0
27
1
52
2
77
x
y
2
9
3
14
4
21
5
30
6
41
x
y
4
27
5
9
6
3
7
1
8
𝟏
𝟑
Inverse Functions: You will need to be able to find an inverse table, graph or equation given the original function in
table, graph or equation form.
Find the inverse function for each list, table, graph and equation given.
5. {(3.4, 8)(7, 9.7)(11, 12.4)(15, 14.1)}
6. 𝑓(𝑥) = 7𝑥 − 2
7. f(x) = 2x + 3
8.
9.
10. Given the following table, create the table for the inverse function.
X
Y
-9
17
-8
8
-7
-1
-6
-10
-5
-19
X
11. Find the inverse function of 𝑓(𝑥) =
12.
Y
𝑥−1
3
Find the inverse function of 𝑓(𝑥) = 3𝑥 − 7
Linear Equations and Systems of Equations
1.) 5𝑛 − 16 − 8𝑛 = −10
2.) 2(𝑥 − 7) = 2(−2𝑥 + 14)
3.) Scientists are interested in the effects of a certain fertilizer on plant growth. They measure a plant’s current
height at 12.6 cm. Each week, the plant grows an additional 1.5 cm.
Define your variables:
Write an equation:
How many weeks until the plant doubles in height? Justify your answer.
4.) The jazz band is putting on a school bake sale. They are selling vanilla cupcakes for $3 and chocolate chip cookies
for $2. At the end of the day, they had made $453.
Define your variables:
Write an equation:
If they sold 97 cupcakes, how many cookies did they sell? Justify your answer.
Solve the following systems of equations by either substitution or elimination.
5.) {
3𝑥 − 4𝑦 = 11
𝑦 = 2𝑥 + 1
6.) {
5𝑥 + 2𝑦 = −1
−6𝑥 + 3𝑦 = −42
7.) {
4𝑥 + 10𝑦 = −10
−2𝑥 + 7𝑦 = 17
8.) {
𝑦 = −2𝑥 + 7
𝑦 = 3𝑥 − 8
Write a system of equations and solve.
9.) Kelly has $30 in her savings and adds another $10 each week. John has $50 in his savings and adds another $5
each week. How long until Kelly and John both have the same amount of money in their savings? How much will
they have at that time?
10.) A local restaurant charges $15 per each adult and $5 per each child to eat at their buffet. Last Saturday night,
the restaurant made $3,380 off of their buffet. If they had 432 total diners, how many were children and how
many were adults?
Exponential Functions
1. Graph the following exponential functions. Use the table if needed.
(a) 𝑦 = 2(3)𝑥
(b) 𝑦 =
16(0.5)𝑥
2. Find the equation for the functions graphed below.
(a)
(b)
3. A house purchased for $226,000 has lost 4% of its value each year for the past five years. What is it worth now?
4. A 1970 comic book has increased in value 10% per year and originally sold for $0.35. What will it be worth in
2010?
5. Ryan's motorcycle is now worth $2500. It has decreased in value 12% each year since it was purchased. If he
bought it four years ago, what did it cost new?
6. A two-bedroom house in Nashville is worth $110,000. If it appreciates at 2.5% per year, what will it be worth in
16 years?
7. You invest $500 dollars into a retirement account when you are 18 years old. The interest rate on your account
is 6.2% and is compounded quarterly. How much is in your account when you retire at the age of 65 years old?
8. A doctor buys a car. The value of the car is modeled by the equation. 𝑦 = 28,000(.91)𝑥 .
a. Define the variables in this function.
b. Describe what you know about the car and its value based on the function.
Properties of Exponents
Simplify each expression.
6. (3𝑥 2 )0
1. (9𝑦 5 )(3𝑦 7 )
7.
2. 7𝑥 −5
(4𝑣 2 )3
8. 𝑏 −1
3. 26𝑦 6 𝑥 −2
9.
𝑥 12
𝑥7
10.
30𝑝3 𝑟 5
6𝑝2 𝑟 8
4. (27𝑎3 𝑏 5 )0
5. 𝑘𝑚 ∙ 3𝑘 4 𝑚2