Changing “a”In this section, the change in “a” will be evaluated in the function f(x) = a|x - h| + k .
The absolute value function f(x) = a | x - h | + k is affected when "a" changes values.
What happens if we change "a" in y = a | x - h | + k ?
To view the affects “a” has on the absolute value function click on the link below and slide the first slider in the lower left hand corner back and forth observing the change in the graph.
Evaluate the function by looking at the table of values.
y = | x |
x |
y |
3 |
-3 |
2 |
-2 |
0 |
0 |
-2 |
-2 |
-3 |
-3 |
and
y = -| x |
x |
y |
3 |
3 |
2 |
2 |
0 |
0 |
-2 |
2 |
-3 |
3 |
**Notice the y – values are all positive in the first graph and all negative in the second graph. When the “a” value is negative the graph faces downward.
y = | x |
x |
y |
2 |
2 |
1 |
1 |
0 |
0 |
-1 |
1 |
-2 |
2 |
and
y = 2 | x |
x |
y |
2 |
4 |
1 |
2 |
0 |
0 |
-1 |
2 |
-2 |
4 |
and
y = 1 2 | x |
x |
y |
2 |
1 |
1 |
1 over 2 1 2 |
0 |
0 |
-1 |
1 over 2 1 2 |
-2 |
1 |
**Notice the y – values, they are double and the graph would be narrower (stretched) in the second table. In the third table, the y – values are halved and the graph would be wider (compressed). When a > 0, the graph is stretched; and when a < 0, the graph is compressed.