Question

If the graph of $y=\mid x\mid$ is shifted to the right by $a$, we get the graph of?

• A. $y=\mid x+a\mid$
• B. $y=\mid x-a\mid$
• C. $y=\mid \frac{x}{a}\mid$
• D. $y=\mid x\mid +a$

Answer 1

The correct option is B $y=\mid x-a\mid$

"If $a$ is a positive real number, then the graph of $f(x-a)$ is the graph of $y=f\left(x\right)$, shifted to the right by $a$ units". The pictorial representation of horizontal shift is shown above.
Let $y=f\left(x\right)=|x|$
When $y=|x|$ is shifted to the right by $a$, we get $y=|x-a|$
Therefore if the graph of $y=|x|$ is shifted to the right by $a$, we get the graph of $y=|x-a|$