Question

Question 2 of 10

If you apply the changes below to the quadratic parent function, f(x) = x2,
what is the equation of the new function?
• Shift 1 unit left.
• Vertically stretch by a factor of 3.
• Reflect over the x-axis.
A. g(x) = -3(x-1)2
B. g(x) = -3(x + 1)2
C. g(x) = (-3x+1)
D. g(x) = -3x2 - 1

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.

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.