Explain how the values of h and k in y=|x-h|+k affect the graph of y=|x|

Horizontal shift:

For the parent function f (x) and a constant h, the function given by g (x) = f (x-h) can be sketched by shifting f (x) h units horizontally.

The values of h determines the direction of shifts:

If:

h>0, the parent graph shifts h units to the right h < 0, the parent graph shifts h units to the left.

Vertical shifts:

For the parent function f (x) and a constant k, the function given by g (x) = f (x) + k can be sketched by shifting f (x) k units vertically.

The value of k determines the direction of shifts;

if:

k > 0, the parent graph shifts k units upward, and k < 0, the parent graph shifts k units downward.

Therefore, the values of h and k in y=|x-h|+k affect the graph of y=|x| tells us how far the graph shifts horizontally and vertically.