Question

While doing the transformation $f\left(x\right)\to |f\left(x\right)|$, we take the mirror image of the graph lying below x-axis and leave the other parts as it is to get the graph of f(x) from |f(x)|

• A. True
• B. False

Answer 1

The correct option is A

True

$|x|=xifx\ge 0$

$=-xifx\le 0$

Similarly,

$|f\left(x\right)|=f\left(x\right)iff\left(x\right)\ge 0$

$=-f\left(x\right)iff\left(x\right)\le 0$

This means, while drawing the graph of |f(x)| from f(x), leave the part where f(x) is positive and change the sign of negative part. Changing the sign $\left(f\right(x)\to -f(x\left)\right)$ is done by taking reflection about x-axis.