Solutions
Name _______________________________
Block ____ Date __________
Algebra: R.2 Functions
Bell Work: What is the domain and range for each function?
y
a.
b.
c.
y
y
(3,5)
5
x
3
Domain: 𝟎 ≤ 𝒙 ≤ 𝟑
Range: 𝟎 ≤ 𝒚 ≤ 𝟓
(5, 3)
x
x
Domain: 𝒙 ∈ ℝ
Range: 𝒚 ≤ 𝟓
Domain: 𝒙 ≤ 𝟓
Range: 𝒚 ≤ 𝟑
𝒉(𝒙)
1. Use functions f, g and h to answer the following questions.
14
𝒇
y
12
10
8
Multiply by 3 and
then subtract 2
6
4
2
𝒙
−12
0 1
2
3
4
−10
−8
−6
−4
𝒈(𝒙) 3 6 12 24 48 96
If 𝑔(𝑥) = 48, then what is 𝑥?
h.
𝒇(𝒙) = 𝟑𝟑 − 𝟐
c.
Classify f
i.
d.
𝑳𝑳𝑳𝑳𝑳𝑳
Write an equation in vertex form for h
j.
e.
𝒉(𝒙) = (𝒙 + 𝟒)𝟐 − 𝟔
What is ℎ(−8)?
k.
Classify h
Classify g
l.
𝑸𝑸𝑸𝑸𝑸𝑸𝑸𝑸𝑸
f.
𝑥=𝟒
= 𝟏𝟏
𝑬𝒙𝒙𝒙𝒙𝒙𝒙𝒙𝒙𝒙𝒙
6
−6
Write an equation for f
b.
4
−4
g.
3(−4) − 2 = −𝟏𝟏
2
−2
What is 𝑓(−4)?
a.
−2
5
x
If ℎ(𝑥) = −2, then what is 𝑥?
𝑥 = −𝟔
What is 𝑔(3)?
𝑥 = −𝟐
= 𝟐𝟐
If 𝑓 (𝑥) = 16, then what is 𝑥? 3𝑥 − 2 = 16
Write an equation for g
𝒈(𝒙) = 𝟑(𝟐)𝒙
3𝑥 = 18
𝒙=𝟔
2. Aura thinks the solution to the systems of equations below is (−2, 4) while Edison thinks the solution is
(2, −2). Teresito thinks they are both wrong. Who is correct? Solve the system to Justify your answer.
3(−2) + 2(4) = 2
5(−2) − 12 = 4 
3𝑥 + 2𝑦 = 2
5𝑥 − 12 = 𝑦
Edison is Correct
3(2) + 2(−2) = 2
5(2) − 12 = −2 
3𝑥 + 2(5𝑥 − 12) = 2
3𝑥 + 10𝑥 − 24 = 2
13𝑥 = 26
𝒙=𝟐
3. Graph the function ℎ(𝑥 ) = −√3 − 𝑥 .
Use inequalities to describe the domain and range.
5(2) − 12 = 𝑦
𝒚 = −𝟐
y
8
6
4
Domain: 𝒙 ≤ 𝟑
Range: 𝒚 ≤ 𝟎
2
x
−8
−6
−4
−2
2
4
6
8
−2
−4
−6
−8
4. If 𝑓(𝑥 ) =
−5
𝑥+2
and g(x) = (x − 2)3, find each output value below (if possible). If it is not possible,
explain why not.
a. f(−2) Not Possible, you can’t divide by 0
b. g(−1) = −𝟐𝟐
c. g(4)
= 𝟖
d. f(−7) + g(1) = 1 + (−1) = 𝟎
e. f(3) − g(2)
= −1 + 0 = −𝟏
5. Write and solve a system of equations to solve the following problem. Be sure to define your
D = the number of dimes
variables and answer the question at the end.
Q = the number of quarters
Jessica has 147 coins that are all dimes and quarters. The number of quarters
is 6 fewer than twice the number of dimes. What is the value of her coins?
𝑫 + 𝑸 = 𝟏𝟏𝟏
𝑸 = 𝟐𝟐 − 𝟔
𝐷 + 2𝐷 − 6 = 147
3𝐷 = 153
𝐷 = 51
𝑄 = 2(51) − 6
𝑄 = 96
Value = 51(. 10) + 96(.25)
= $𝟐𝟐. 𝟏𝟏
PARCC Prep
6.
2
7.
y
8
x
2
0
y
0
-3
6
4
2
x
−8
−6
−4
2
−2
4
6
8
−2
−4
−6
−8
8.
𝑏(0) = 4(2)0 = 4
∆𝑏
𝑏(5) = 4(2)5 = 128
Δ𝑏 124
𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏
=
= 24.8 𝑚𝑚𝑚𝑚𝑚𝑚
5
Δ𝑡
9. Use a graph in calculator to solve the system of equations.
Write solution(s) in (x, y) form. Make a sketch of the graph
with the solutions labeled. (hint: enlarge the window!)
y = x2 − x + 12
y = 2x2 + 3x + 7
y
(−5, 42)
(1, 12)
x
10. Write an equation for f(x).
𝒇(𝒙) = −(𝒙 − 𝟏)𝟐 + 𝟒
11. Solve each equation or inequality below, if possible by using graphs.
a.
−(x − 3)(x + 1) = 4
y
1
𝒙=𝟏
12.
b. |𝑥 − 3| > 4
c. (x − 5)3 = 8
y
x
−1
y
x
x
7
7
𝒙 < −𝟏 or 𝒙 > 𝟕
𝒙=𝟕
Graph the parent function 𝑦 = |𝑥| (dotted) and then graph
𝒇(𝒙) = |𝒙 − 𝟑| − 𝟏 (solid) by transforming the parent.
Label the vertex, intercepts and roots on the graph of f.
y
8
6
4
2
x
−8
−6
−4
−2
2
4
6
8
−2
(3, −1)
Vertex
Roots(x-intercepts):
𝒙 = 𝟐, 𝒙 = 𝟒
−4
𝒚 intercept: 𝒚 = 𝟐
−6
−8