Algebra 2 – Unit 2 Summary
Name:_____________________
Absolute Value Functions
Block:______________
1) Consider the function y   x  4  3
a) Graph the function.
b) State the domain and range for the function.
c) Describe the shifts in relation to the parent function:
d) Is the inverse of the function a function? Why or why not?
e) Find the x-intercepts of the function:
2) Graph the functions.
 1
 3 x  4,
b) g ( x )  
 2 x  1,
 3
3x  5, x  3

a) f ( x)  2,
3 x 5
 x,
x5

x  3
x  3
3) Write a piecewise function that corresponds with the following graph and identify the following:
Domain:
Range:
Increasing:
Decreasing:
Discontinuities:
x  , f ( x )  _______
x  , f ( x )  ______
4) A company provides bus tours of historical cities. The given function describes the rate for small
groups and the discounted rate for larger groups, where x is the number of people in your group.
C(x)
8.95𝑥, 𝑖𝑓 0 < 𝑥 ≤ 10
𝐶= {
7.50𝑥,
𝑖𝑓 𝑥 > 10
Graph the function. Identify the Domain and Range
5) 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?
6) Write an equation for each graph describe:
a. a V-shaped that is shifted down 4 units:_________________________________
b. a V-shaped graph that is shifted right two units and up one unit:
________________________________
7) Describe the transformation for the parent function 𝑓(𝑥) = |𝑥|:
a. 𝑔(𝑥) = −5|𝑥 + 7| ________________________________________________________
b. ℎ(𝑥) = |𝑥| + 3
_______________________________________________________
Solve and graph each of the following. State the solution set in interval notation.
1
3
8) 2 3 x  5  15
9)  x  3  6
10) x  1  4
2
4
Graph each of the following using a table of values and determine the solution set:
1
11) y  2 x  4
12) y  2 x  2
13) y  x  4  3
2
solution(s) set:____________
solution(s) set:____________
solution(s) set: ____________