Question

For the graph of the parent function y = |x|, what happens when we write y = a|x| when a > 1?

a) Vertical compression
b) Vertical stretch
c) Horizontal compression
d) Horizontal stretch

Answer 1

When the parent function y = |x| is changed to y = a|x| where a > 1, it causes a vertical stretch because the factor 'a' multiplies the output, making the graph steeper.

Step-by-step explanation:

When we modify the parent function y = |x| to y = a|x| where a > 1, the graph of the function undergoes a vertical stretch. This is because the value of 'a' acts as a vertical scalar that stretches the graph away from the x-axis, making it steeper than the original parent function. This transformation does not affect the horizontal dimensions of the graph, so there is no horizontal compression or stretch. Therefore, each point on the original graph moves vertically upward in the coordinate system by a factor of 'a', while retaining its horizontal position.