Question

Step 1

*Given:*

The function is,

Step 2

To sketch the graph of the function g(x), using transformation as shown in the following graphs.

Consider the function *y = x²* .

Substitute the values* x* = 0, *x* = 2 and *x* = –2 in the above function.

Then the corresponding *y* values are y = 0, y = 4 and y = 4.

That is, the points required to draw the graph *y = x²* are (0,0), (–2,4) and (2,4).

Sketch the graph *y* = *x*² as shown in the below figure.

Step 3

Translate the function *y = x*² by the left of 1 unit.

Then the translation function is *y = *(*x+1*)² .

Substitute the values* x* = –1, *x* = –4 and *x* = 2 in the above function.

Then the corresponding *y* values are y = 0, y = 9 and y = 9.

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