Question

On a separate sheet of paper, use the graph of y = |x| to graph y+4=|x| In the answer box, explain how the new graph differs from the parent function.

Answer 1

The new graph (solid blue) is shifted 4 units down from the parent function (dashed red).

You can get there a couple of ways:

Replacing y by y-k shifts the graph up by k units. Here, k=-4, so the graph is shifted down 4 units.

Adding k to the function value shifts the graph vertically by k units. The equation y+4 = |x| can be rewritten to y = |x| -4, showing that -4 is added to the function value.

Explanation:

Answer 2

See the attachment for graphs.

Explanation:

The new graph (solid blue) is shifted 4 units down from the parent function (dashed red).

You can get there a couple of ways:

1. Replacing y by y-k shifts the graph up by k units. Here, k=-4, so the graph is shifted down 4 units.
2. Adding k to the function value shifts the graph vertically by k units. The equation y+4 = |x| can be rewritten to y = |x| -4, showing that -4 is added to the function value.