Question

Which function is the result of vertically shrinking ƒ(x) = 2(x + 3)2 by a factor of ½ and reflecting it across the x-axis?

Question 7 options:

A)

y = (x + 3)2

B)

y = –½(x + 3)2

C)

y = –(x + 3)2

D)

y = ½(x + 3)2

Answer 1

C) y = -(x + 3)2

Explanation:

To vertically shrink the function by a factor of 1/2, we just need to multiply f(x) by 1/2 (This way the values in the y-axis will decrease by a factor of 1/2):

`y = (1/2) * 2(x + 3)^2`

`y = (x + 3)^2`

Now, to reflect the function across the x-axis, we just need to put a minus sign in the front of the function (so the values in the first and second quadrant will go to the third and fourth quadrant, that is, f(x) will be -f(x)):

`y = -(x + 3)^2`

So the correct option is C)