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Question

Identify the graph of |x+3|


A

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B

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C

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D

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Solution

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| |x+3| |x+3| |(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(x),f(x+a),f(x) etc.

(1) |x| |x+3|

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

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

(2) |x+3| |x+3|

when f(x) becomes f(x) ,we take the reflection about x-axis.

(3) |x+3| |(x)+3|

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


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