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Question #3, Section 3.5 A.)Let f(x) = (x-3)^2. Find f(-x) and -f(x). f(-x)= -f(x)= Is f(x)...

Question #3, Section 3.5
A.)Let f(x) = (x-3)^2. Find f(-x) and -f(x).
f(-x)=
-f(x)=
Is f(x) odd, even, or neither?

B.) Let f(x) = Squareroot(x). Find g(x), the function that is f(x) reflected over the x-axis and horizontally stretched by a factor of 5.
g(x)=

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Answer #1

A)

f(x) = (x-3)2 = x2 + 9 - 6x

f(-x) = (-x-3)2 = (x+3)2 = x2 + 9 + 6x

-f(x) = - (x-3)2 = -(x2 + 9 - 6x)

As f(-x) ≠ f(x) and f(-x) ≠ -f(x), it is neither odd nor even.

B)

f(x) = √x

Taking image about X-axis

f'(x) = -√x

Horizontal stretching by factor of 5

f'(x) = g(x) = (-1/5)√x

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