Question

Describe the transformation

from the parent function
p(x) = |x| ,f(x) = |3x|

A) Horizontal stretch by a factor of 3 and reflection across the y-axis
B) Vertical compression by a factor of 3 and translation to the right
C) Vertical stretch by a factor of 3 and translation to the left
D) No transformation is applied; it's the same as the parent function

Answer 1

The transformation from the parent function p(x) = |x| to f(x) = |3x| is a vertical compression by a factor of 3 and a translation to the right.

Step-by-step explanation:

The transformation from the parent function p(x) = |x| to f(x) = |3x| is a vertical compression by a factor of 3 and a translation to the right.

To explain this transformation, we need to understand that the parent function p(x) represents the absolute value of x, which is a V-shaped graph symmetric to the y-axis.

When we multiply the function by 3, it compresses the graph vertically, making it narrower. And when we replace x with 3x, it translates the graph to the right by dividing the x-values by 3. So, the transformation is a vertical compression by a factor of 3 and a translation to the right.