Question

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

Answer 1

Answer:

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.