Is the following function even, odd, or neither? f(x)=5x Choose 1 answer: (A) Even (B) Odd (c) Neither

Symmetry properties of the function: To determine if the function f(x) = 5x is even, odd, or neither, we need to check the symmetry properties of the function. An even function satisfies the condition f(x) = f(-x) for all x in its domain, while an odd function satisfies the condition f(-x) = -f(x) for all x in its domain.Checking if f(x) is even: Let's check if f(x) is even. We substitute -x for x in the function and see if it equals f(x): f(-x) = 5(-x) = -5x. Now we compare this to f(x): f(x) = 5x. Since f(-x) does not equal f(x), the function is not even.Comparing f(-x) and f(x): Next, let's check if f(x) is odd. We already have f(-x) = -5x from the previous step. Now we compare this to -f(x): -f(x) = -5x. Since f(-x) equals -f(x), the function is odd.

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Is the following function even, odd, or neither?

f(x)=5x
Choose 1 answer:
(A) Even
(B) Odd
(c) Neither

Is the following function even, odd, or neither? $\newline$ $f(x)=5 x$ $\newline$ Choose $1$ answer: $\newline$ (A) Even $\newline$ (B) Odd $\newline$ (C) Neither

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Algebra 2

Symmetry and periodicity of trigonometric functions

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Q. Is the following function even, odd, or neither?

\newline

f(x)=5 x

\newline

Choose

1

answer:

\newline

(A) Even

\newline

(B) Odd

\newline

Symmetry properties of the function: To determine if the function $f(x) = 5x$ is even, odd, or neither, we need to check the symmetry properties of the function. An even function satisfies the condition $f(x) = f(-x)$ for all $x$ in its domain, while an odd function satisfies the condition $f(-x) = -f(x)$ for all $x$ in its domain.
Checking if $f(x)$ is even: Let's check if $f(x)$ is even. We substitute $-x$ for $x$ in the function and see if it equals $f(x)$ : $f(-x) = 5(-x) = -5x.$ Now we compare this to $f(x)$ : $f(x) = 5x.$ Since $f(-x)$ does not equal $f(x)$ , the function is not even.
Comparing $f(-x)$ and $f(x)$ : Next, let's check if $f(x)$ is odd. We already have $f(-x) = -5x$ from the previous step. Now we compare this to $-f(x)$ : $-f(x) = -5x$ . Since $f(-x)$ equals $-f(x)$ , the function is odd.