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

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):

[tex]y = (1/2) * 2(x + 3)^2[/tex]

[tex]y = (x + 3)^2[/tex]

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)):

[tex]y = -(x + 3)^2[/tex]

So the correct option is C)

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

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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