Question

Select the correct answer. Each statement describes a transformation of the graph of y = x. Which statement correctly describes the graph of y = x − 8? A. It is the graph of y = x translated 8 units down. B. It is the graph of y = x translated 8 units to the left. C. It is the graph of y = x where the slope is decreased by 8. D. It is the graph of y = x translated 8 units up.

Answer 1

A. correctly describes the transformation of the graph of y = x - 8 as a translation 8 units down.

Explanation:

the constant is 8, so the graph of y = x - 8 is obtained by moving the graph of y = x downward by 8 units.

the constant is 8, so the graph of y = x - 8 is obtained by moving the graph of y = x downward by 8 units.

to visualize this, imagine the original graph of y = x. If you were to pick any point on this graph and subtract 8 from its y-coordinate, you would get the corresponding point on the graph of y = x - 8.

For example, the point (2, 2) on the graph of y = x would become (2, -6) on the graph of y = x - 8.

Option A correctly describes the transformation of the graph of y = x - 8 as a translation of 8 units downward.

On the graph of y = x - 8, the point (2, 2) would become (2, -6).

Option A correctly describes the graph of y = x - 8 as a vertical translation of 8 units downward.

Glad to help :)