Question

Question 2 of 10

Answer 1

Given:

The parent function is:

$f(x)=x^2$

This function shift 1 unit left, vertically stretch by a factor of 3 and reflected over the x-axis.

To find:

The function after the given transformations.

Step-by-step explanation:

The transformation is defined as

$g(x)=kf(x+a)+b$                ... (i)

Where, k is stretch factor, a is horizontal shift and b is vertical shift.

If k<0, then the graph of f(x) is reflected over the x-axis.

If 0<|k|<1, then the graph compressed vertically by factor |k| and if |k|>1, then the graph stretch vertically by factor |k|.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

It is given that the graph of f(x) shifts 1 unit left, so a=1.

The graph of f(x) vertically stretch by a factor of 3, so |k|=3.

The graph of f(x) reflected over the x-axis, so k=-3.

There is no vertical shift, so b=0.

Putting $a=1,k=-3,b=0$ in (i), we get

$g(x)=-3f(x+1)+0$

$g(x)=-3f(x+1)$

$g(x)=-3(x+1)^2$                     $[\because f(x)=x^2]$

Therefore, the correct option is B.