Question

What transformations produce the graph of g(x)=- | 3x | from the graph of the parent function f(x)=|x| Select all that apply

Answer 1

This would be a reflection over the x-axis and a vertical stretch by a factor of 3.

Explanation:

We can identify the shift over the x-axis by looking at the negative in the front.

We can identify the vertical stretch by noting that the variable is being multiplied by 3, which makes the y value go up 3 times as fast.

Answer 2

Horizontal compression by a factor of 3.

Reflection over the x-axis.

Explanation:

The parent function is

`f(x)=|x|`

The transformed function is

`g(x)=-|3x|`

Notice that the transformation involves to multiply the function with -1 and multiply the independent variable by 3.

Remember, if we multiple the independent variable by a number greater than 1, then the function will compress horizontally, that is, in the direction of x-axis.

Additionally, if we multiply the function by a negative number as -1, the function graph will reflect across the x-axis.

The image attached shows these transfomations.

Therefore, the right answers are:

• Horizontal compression by a factor of 3.
• Reflection over the x-axis.