219k views
2 votes
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

1 Answer

6 votes

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.

User PurTahan
by
9.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories