Sharp EL-9650 Shifting a graph of Absolute Value Functions, x if x ≥, Example, y =xchanges to y =

EL-9650/9600c/9450/9400 Graphing Calculator

Shifting a graph of Absolute Value Functions

The absolute value of a real number x is defined by the following:

x =	x if x ≥	0
	-xif x ≤	0

If n is a positive number, there are two solutions to the equation f (x) = n because there are exactly two numbers with the absolute value equal to n: n and -n.The existence of two distinct solutions is clear when the equation is solved graphically.

An absolute value function can be presented as y = ax - h+ k. The graph moves as the changes of slope a, x-intercept h, and y-intercept k.

Example

Move and change graphs of absolute value function y =x to check the relation between the graphs and the values of coefficients.

1. Move the graph y = x downward by 2 using the Shift feature.

2. Move the graph y = x to the right by 2 using the Shift feature.

3. Pinch the slope of y = x to 2 or minus using the Change feature.

Before There may be differences in the results of calculations and graph plotting depending on the setting. Starting Return all settings to the default value and delete all data.

Step & Key Operation	Display	Notes
(When using EL-9650/9600c)	(When using EL-9650/9600c)
*Use either pen touch or cursor to operate.

1-1Access the Shift feature. Select y = x.

2nd F SHIFT/CHANGE A *

( ENTER ALPHA * ) 8 *

1-2Move the graph downward by 2.

ENTER *

1-3Save the new graph and look at the relationship of the function and the graph.

ENTER ALPHA

y=xchanges to y = x-2

The graph of the equation that is highlighted is shown by a solid line. Notice that the y- intercept k in the standard form y = ax - h+ k takes charge of vertical movement of the graph.

8-2