consider this function and its graph. f(x)=tan(3x+π/4)-1 which statement best describes function f? a. the…

consider this function and its graph. f(x)=tan(3x+π/4)-1 which statement best describes function f? a. the function is odd. b. the function is even. c. the function is neither even nor odd. d. there is not enough information to determine whether the function is even or odd.

consider this function and its graph. f(x)=tan(3x+π/4)-1 which statement best describes function f? a. the function is odd. b. the function is even. c. the function is neither even nor odd. d. there is not enough information to determine whether the function is even or odd.

Answer

Explanation:

Step1: Recall odd - even function definitions

An even function satisfies $f(x)=f( - x)$ for all $x$ in the domain, and an odd function satisfies $f(-x)=-f(x)$ for all $x$ in the domain.

Step2: Find $f(-x)$

Given $f(x)=\tan(3x +\frac{\pi}{4})-1$. Then $f(-x)=\tan(- 3x+\frac{\pi}{4})-1$. Using the identity $\tan(-\alpha)=-\tan(\alpha)$, we have $f(-x)=-\tan(3x - \frac{\pi}{4})-1$.

Step3: Find $-f(x)$

$-f(x)=-\tan(3x+\frac{\pi}{4}) + 1$.

Step4: Compare

Since $f(-x)\neq f(x)$ (because $-\tan(3x - \frac{\pi}{4})-1\neq\tan(3x+\frac{\pi}{4})-1$) and $f(-x)\neq - f(x)$ (because $-\tan(3x - \frac{\pi}{4})-1\neq-\tan(3x+\frac{\pi}{4}) + 1$), the function is neither even nor odd.

Answer:

C. The function is neither even nor odd.