Transformations of absolute value 9-22 class notes

Homework for 9-23:  page 28-29, items 15a, 15b, 16a, 16b, 16c

Hints for homework:  Ask these questions:

Will the graph shift left or right?

Will the slopes of the pieces change?

Will the graph flip?

Will the graph shift up or down?

The parent absolute value function has two pieces, a left piece with a slope of -1 and a rightpiece with an opposite slope of 1.

The parent absolute value function's vertex is neither high or low because the point of the V is at (0,0).

The parent absolute value function's vertex is neither left or right because the point of the V is at (0,0).

If you subtract something (minus a positive) from x inside the absolute value bars, the graph shifts right
y = | x - 3 |                                       moves the parent function to the right.



If you add something (minus a negative) to x  inside the absolute value bars, the graph shifts left
y = | x - 2 | means y = | x - (-2) |      moves the parent function to the right.

If you multiply the absolute value part by a number, you change the slopes of the pieces.
item 11 from the homework, y = 3 | x | gives a graph with a sharper V

If you multiply the absolute value part by a negative number, you flip (invert) the graph.
y = -2 | x | gives a graph where the V points up instead of down

If you add something outside the absolute value bars, the graph shifts to a higher position
 y = | x | + 4                                     moves the vertex of the parent function up 4

If you subtract something outside the absolute value bars, the graph shifts to a lower position
 y = | x | - 4                                     moves the vertex of the parent function down 4