Question

Describe the effects on the linear parent function when f(x) is changed to -3f(x) or f(-3x).

a) The function is vertically stretched by a factor of 3.
b) The function is vertically compressed by a factor of 3.
c) The function is reflected over the x-axis and then vertically stretched by a factor of 3.
d) The function is reflected over the y-axis and then horizontally stretched by a factor of 3.

Answer 1

When f(x) is changed to -3f(x), the function is vertically compressed by a factor of 3. When f(x) is changed to f(-3x), the function is reflected over the y-axis and then horizontally stretched by a factor of 3.

Step-by-step explanation:

When the linear parent function f(x) is changed to -3f(x), the function is vertically compressed by a factor of 3. This means that the graph of the function becomes narrower, as the y-values are scaled down by a factor of 3.

On the other hand, when f(x) is changed to f(-3x), the function is reflected over the y-axis and then horizontally stretched by a factor of 3. This means that the graph of the function is flipped to the opposite side of the y-axis, and then becomes wider, as the x-values are scaled up by a factor of 3.