Page 737 - Algebra 1

Example
2
Translating Absolute-Value Graphs
Graph the function and give the coordinates of the vertex.
a. f(x)=⎢x -2
SOLUTION
Use a table to graph the function.
The graph of the parent function is translated down 2 units. The vertex is (0, -2).
b. f(x)=⎢x+3
SOLUTION
Use a table to graph the function.
The graph of the parent function is translated left 3 units. The vertex is (-3, 0).
x
-3
-2
-1
0
1
2
3
y
1
0
-1
-2
-1
0
1
x
-6
-3
0
3
6
y
3
0
3
6
9
Multiple Translations of Absolute-Value Graphs
Vertical and Horizontal Translation
If a constant h is subtracted inside the absolute-value bars and a constant k is added outside the bars, as in f(x) = ⎢x - h + k. The graph is translated both vertically and horizontally. The vertex is
at (h, k).
The graph of f(x) = ⎢x - h + k, where h = 1 and k = 1, is shown.
y
8
4
O
x
-8
-4
4
8
-4
-8
Graphing Multiple Translations
Graph the function and give the coordinates of the vertex. f(x) = ⎢x - 4 + 1
SOLUTION
The graph of the function is determined by translating the parent function. Evaluate how the function is different from the parent function.
The vertex is (4, 1).
Example
3
Hint
Knowing how to translate the graph of
y = ⎢x using h and k can replace the use of a table of values to find points on the graph.
722 Saxon Algebra 1
y
8
4
O
x
-8
-4
4
8
-4
-8
y
8
4
O
x
-8
-4
4
8
-4
-8
y
8
4
O
x
-8
-4
4
8
-4
-8