Algebra 2
Unit 1 Review
Name _________________________________
Solve each equation for a.
1)
6(a  4)  12  2(a  5)
2)
a4
2 y
3
3)
3(𝑎−4)
3
= 5𝑎 + 2
4) The width of a rectangle is 6 cm less than its length. The perimeter is at the most 124 cm.
a)
Write an equation representing the width in terms of the length.
b)
Find the possible solutions for the length and the width.
Solve each of the following inequalities. Graph your solutions.
5) 4y – 3 < 6y – 5
6) -2 < 6 – 2x < 10
7) 2𝑥 ≤ −16 𝑜𝑟 3𝑥 > 27
8) Which relations are functions?
9) Use the relation below to answer the following questions.
{(-2, 6), (5, -2), (-3, 6), (4, 0), (9, 5)}
a)
Express the domain: _______________________________________________
b)
Express the range: ___________________________________________________
c)
Is the relation a function? Yes or No
Use the graphs below to answer the following questions:
a) Is the graph a function?
b) Express the domain as an inequality.
10)
11)
12) Describe the transformation need to change 𝒚 = 𝒇(𝒙) into 𝒚 = 𝒇(𝒙 + 𝟐) − 𝟒.
13) Consider and evaluate the graph of f(x) on the right:
f(0)=_____
f(10)=_____
f(8)=_____
f(-7)=_____
f(5)=_____
f(x)=-8, x=_____
f(1)=_____
f(x)=-6, x=_____
f(x)=-2, x=_____
14) Use the functions given below to perform the operations:
𝒇(𝒙) = 𝟖𝒙 − 𝟑
𝒈(𝒙) = 𝟓𝒙𝟐
𝒉(𝒙) = 𝟒𝒙 + 𝟏𝟎
a) f(x) + h(x)
b) g(x) - f(x)
c) f(x) * h(x)
e) 4h(x)
f) h(f(x))
g) g(f(-1))
d) g(3) + h(-2)
15) Given the following graph representing 𝒚 = 𝒇(𝒙), complete the following problems. Use a table if needed.
𝒚 = 𝒇(𝒙)
c)
Graph 𝒚 = 𝟐𝒇(𝒙)
a) Graph 𝒚 = −𝒇(𝒙)
b) Graph 𝒚 = 𝒇(𝒙 − 𝟐)
d) Graph 𝒚 = 𝒇(𝒙) − 𝟒
16. Consider the following functions:
𝒇(𝒙) = 𝟓𝒙𝟐 − 𝟖𝒙 + 𝟏𝟒
Evaluate: 𝒇(−𝟒) =
𝟏𝟓𝒙−𝟖
𝒈(𝒙) = 𝟕(𝒙+𝟑)−𝟒(𝒙−𝟐)
𝒈(𝟔) =
17. Use the graph of f(x) and g(x) to find the following values.
f(x)
g(x)
a. 𝒇(𝒈(𝟎))
b. 𝒇(𝒇(−𝟑))
c. 𝒈(𝒇(𝟑))
d. 𝒈(𝒈(−𝟔))
e. 𝒇(𝒈(𝟏))
18. Let 𝒇(𝒙) = −𝟒𝒙, 𝒈(𝒙) = 𝒙𝟐 , and 𝒉(𝒙) = −𝒙 − 𝟏.
a. 𝒇(𝒙) =
b. 𝒇(𝒈(𝒙)) =
c. 𝒇(𝒈(𝟐)) =
d. 𝒉(𝒇(𝒙)) =
e. 𝒉(𝒉(𝒙)) =
f. 𝒈(𝒇(−𝟑))
g. 𝒇(𝒙) − 𝒉(𝒙)
h. 𝒈(𝒙) − 𝒉(𝒙)