Question

Graph of $|f\left(|x|\right)|$ is obtained from f(x) through the following steps.

1. Take the reflection of the part of f(x) which is below x-axis

2. Remove the part on negative x-axis

3. Take the reflection of the remaining part about y-axis

• A. True
• B. False

Answer 1

The correct option is A

True

We want to get $|f\left(|x|\right)|$ from f(x). We can either do the transformation

$f\left(x\right)\to f\left(|x|\right)\to |f\left(|x|\right)|$

or

$f\left(x\right)\to |f\left(x\right)|\to |f\left(|x|\right)|$

When we do the transformation $f\left(x\right)\to |f\left(x\right)|$, we make the negative value (part below x-axis) positive by taking reflection about x-axis. The transformation $|f\left(x\right)|\to |f\left(|x|\right)|$, is done by removing the part on negative x-axis and taking a reflection about y-axis of the part in the positive x-direction.

So the three steps in series will give |f(|x|)| from f(x).