Question
How does the graph change from f(x)=|x|
to f(x)=|0.5x|
?(1 point)
The graph is horizontally stretched by a factor of
.
to f(x)=|0.5x|
?(1 point)
The graph is horizontally stretched by a factor of
.
Answers
GPT-4o mini
To understand how the graph of \( f(x) = |x| \) changes to \( f(x) = |0.5x| \), we need to analyze the effect of the factor inside the absolute value.
The general form \( f(x) = |kx| \) results in a horizontal stretch or compression, depending on the value of \( k \):
- If \( |k| < 1 \), the graph is horizontally stretched by a factor of \( \frac{1}{|k|} \).
- If \( |k| > 1 \), the graph is horizontally compressed by a factor of \( \frac{1}{|k|} \).
In this case, since \( k = 0.5 \):
1. Calculate \( \frac{1}{|0.5|} = \frac{1}{0.5} = 2 \).
Thus, the graph of \( f(x) = |0.5x| \) is horizontally stretched by a factor of \( 2 \).
So the answer is:
The graph is horizontally stretched by a factor of \( 2 \).
The general form \( f(x) = |kx| \) results in a horizontal stretch or compression, depending on the value of \( k \):
- If \( |k| < 1 \), the graph is horizontally stretched by a factor of \( \frac{1}{|k|} \).
- If \( |k| > 1 \), the graph is horizontally compressed by a factor of \( \frac{1}{|k|} \).
In this case, since \( k = 0.5 \):
1. Calculate \( \frac{1}{|0.5|} = \frac{1}{0.5} = 2 \).
Thus, the graph of \( f(x) = |0.5x| \) is horizontally stretched by a factor of \( 2 \).
So the answer is:
The graph is horizontally stretched by a factor of \( 2 \).