Is the following function even, odd, or neither? f(x)=4x+2 Choose 1 answer: (A) Even (B) Odd (C) Neither

Definition of Even, Odd, Neither: To determine if the function f(x) is even, odd, or neither, we need to compare f(x) with f(-x). If f(-x) = f(x), then the function is even. If f(-x) = -f(x), then the function is odd. If neither condition is met, the function is neither even nor odd.Calculate f(-x): First, we calculate f(-x) by substituting -x for x in the function f(x)=4x+2. f(-x) = 4(-x) + 2 = -4x + 2Compare f(-x) with f(x): Now we compare f(-x) with f(x). f(x) = 4x + 2 f(-x) = -4x + 2 We can see that f(-x) is not equal to f(x) because f(-x) has a -4x term while f(x) has a 4x term. Therefore, the function is not even.Check if f(-x) is negative of f(x): Next, we check if f(-x) is the negative of f(x). -f(x) = -(4x + 2) = -4x - 2 f(-x) = -4x + 2 We can see that f(-x) is not equal to -f(x) because f(-x) has a +2 term while -f(x) has a -2 term. Therefore, the function is not odd.

Home

Math Problems

Algebra 2

Even and odd functions

Full solution

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

\newline

f(x)=4x+2

\newline

Choose

1

answer:

\newline

(A) Even

\newline

(B) Odd

\newline

Definition of Even, Odd, Neither: To determine if the function $f(x)$ is even, odd, or neither, we need to compare $f(x)$ with $f(-x)$ . If $f(-x) = f(x)$ , then the function is even. If $f(-x) = -f(x)$ , then the function is odd. If neither condition is met, the function is neither even nor odd.
Calculate $f(-x)$ : First, we calculate $f(-x)$ by substituting $-x$ for $x$ in the function $f(x)=4x+2$ . $\newline$ $f(-x) = 4(-x) + 2 = -4x + 2$
Compare $f(-x)$ with $f(x)$ : Now we compare $f(-x)$ with $f(x)$ .
$f(x) = 4x + 2$
$f(-x) = -4x + 2$
We can see that $f(-x)$ is not equal to $f(x)$ because $f(-x)$ has a $-4x$ term while $f(x)$ has a $f(x)$ $1$ term. Therefore, the function is not even.
Check if $f(-x)$ is negative of $f(x)$ : Next, we check if $f(-x)$ is the negative of $f(x)$ .
$-f(x) = -(4x + 2) = -4x - 2$
$f(-x) = -4x + 2$
We can see that $f(-x)$ is not equal to $-f(x)$ because $f(-x)$ has a $+2$ term while $-f(x)$ has a $f(x)$ $1$ term. Therefore, the function is not odd.