Name:
Test Date:
Algebra 2
Absolute Value Test Review Guide
1) Consider the function y = − x + 4 + 3
a) Graph the function on the right.
b) State the domain and range for the function.
Domain:
Range:
c) Describe the shifts in relation to the parent function:
d) Is the inverse of the function a function? Why or why not?
e) State the increasing and decreasing interval.
Increasing:
Decreasing:
f) Identify the x-intercepts (zeroes) of the function:
2) Graph the piecewise functions.
⎧−3x + 5, x < 3
⎪
a) f ( x) = ⎨2,
3≤ x <5
⎪ x,
x≥5
⎩
⎧ 1
⎪⎪− 3 x − 4,
b) g ( x) = ⎨
⎪ 2 x + 1,
⎪⎩ 3
x ≤ −3
x > −3
3) Without using a calculator, graph the function f(x) = 2|x – 1| - 3 a) What is the shape of the graph?
b) What is the vertex of the graph?
c) Does it open up or down? Explain why:
d) What are the slopes of the two lines that create the graph?
e) What is the domain and range of the graph?
Domain:
Range:
4) Write an equation for each graph described below:
a) An absolute value graph that is shifted down 4 units: ________________________
b) An absolute value graph that is shifted right two units and up one unit:
______________________
5) Describe the transformation(s) for the parent function 𝑓 𝑥 = 𝑥 :
a. 𝑔 𝑥 = −5 𝑥 + 7
b. ℎ 𝑥 = 𝑥 + 3
______________________________________________________
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Solve each of the following.
6) 2 3𝑥 − 5 = 16
9) 4𝑥 + 1 = 10𝑥
7) −2 𝑥 − 4 + 3 = 13
8) 2 𝑥 − 6 − 5 = 15
(check for extraneous!)
Solve the absolute value inequalities. Write your answer in both set builder and
interval notation. Graph your answer.
Equation
1
10) − 𝑥 − 3 > 6
2
11)
4
5
𝑥−1 ≤4
12) 3 𝑥 + 4 > 27
13) 2𝑥 − 10 + 1 ≤ 9
Graph on
Number Line
Interval
Notation
Set Builder Notation
14) Transform the following piecewise function.
Original points:
x
a) −3 ∙ 𝑓 𝑥
x
y
y
b) 𝑓 𝑥 + 1 − 2
x
y
15) What does “absolute value” mean? How is solving an absolute value equation
different from solving a regular equation?
16) Explain how the graphical transformations of a given parent function are
evident in the equation of the function. (a, h, and k – what do each of those do?)
17) Describe the domain and range of absolute value functions.