Question

How does the graph change from f(x)=|x|
to f(x)=0.8|x|
? Enter your response as a decimal if appropriate.(1 point)
The graph is a vertical compression by a factor of
.

Answer 1

To understand how the graph changes from \( f(x) = |x| \) to \( f(x) = 0.8|x| \), we need to examine the effect of the coefficient in front of the absolute value function.

The transformation from \( f(x) = |x| \) to \( f(x) = 0.8|x| \) indicates that the graph is vertically compressed. The factor of \( 0.8 \) means that the output values of the function \( f(x) \) are reduced to \( 80\% \) of their original values for any \( x \).

To find the factor of vertical compression, we can express it as follows:

\[
\text{Vertical compression factor} = \frac{1}{0.8} = 1.25
\]

Therefore, the graph of \( f(x) = 0.8|x| \) is a vertical compression of the graph \( f(x) = |x| \) by a factor of \( 0.8 \).

So the answer is:
The graph is a vertical compression by a factor of \( \frac{1}{0.8} = 1.25 \).