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?

Answer 1

Answer:

C) y = -(x + 3)2

Step-by-step 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)