Question

Identify the graph of $-|-x+3|$

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

We will start with $|x|$ and reach $-|(-x)+3|$ through a series of transformation.
The transformations we will follow are $|x|\to |x+3|\to -|x+3|\to -|(-x)+3|$

There are three steps in this. All the individual steps are the simple linear transformations we already did. The idea is to get $-|-x+3|$ from $|x|$ through transformations like $-f\left(x\right),f(x+a),f(-x)$ etc.

(1) $|x|\to |x+3|$

we know when $f\left(x\right)$ becomes $f(x+3)$,the graph of $f(x+3)$ will shift by 3 units to the left.so the

transformation corresponding to $|x|\to |x+3|$ in groups will be

(2) $|x+3|\to -|x+3|$

when $f\left(x\right)$ becomes $-f\left(x\right)$ ,we take the reflection about x-axis.

(3) $-|x+3|\to -|(-x)+3|$

In the transformation x becomes -x.i.e.,$f\left(x\right)\to f(-x)$.we will take the reflection about y-axis