Question

Determine whether the function below is an even function, an odd function, both, or neither.

f(x) = (x+5)^2

Answer 1

using a graphical tool
See attached file
f(x) = (x+5)^2

if f(-x) = f(x) the function is even.
x=-5
f(-x)=(5+5)^2=100
f(x)=(-5+5)^2=0
the function is not even

if f(-x) = -f(x) the function is odd
x=-5
f(-x)=(5+5)^2=100
-f(x)=(-5+5)^2=0
the function is not odd
The answer is neither

Answer 2

A function is even if, for each x in the domain of f, f (- x) = f (x). The even functions have reflective symmetry through the y-axis. A function is odd if, for each x in the domain of f, f (- x) = - f (x). The odd functions have rotational symmetry of 180º with respect to the origin.
f (x) = (x + 5) ^ 2
f (x) = x ^ 2 + 10x + 25
f (-x) = (-x + 5) ^ 2
f (x) = x ^ 2 - 10x + 25
the function does not comply with the definitions.
The function is NOT even
The function is not odd
answer
neither