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Katen [24]
3 years ago
9

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

Mathematics
2 answers:
Ad libitum [116K]3 years ago
4 0
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
coldgirl [10]3 years ago
4 0
 <span>using a graphical tool
</span><span>See attached file
</span><span>f(x) = (x+5)^2
</span><span>
if f(-x) = f(x) the function is even.
x=-5
</span>f(-x)=(5+5)^2=100
f(x)=(-5+5)^2=0
the function is not even

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

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