IB Mathematics Analysis and Approaches Question Type 1: Verifying Whether Some Simple Functions Are Odd or Even or Neither Exercises

Determine whether the function $f(x)=x^4-x^2$ is odd, even, or neither. Justify your answer.

Determine whether the function $f(x)=\cos (x)\sin (x)$ is odd, even, or neither. Justify your answer.

Determine whether the function $f(x)=\sin (x)+\cos (x)$ is odd, even, or neither. Justify your answer.

Determine whether the function $f(x)=x^3+x$ is odd, even, or neither. Justify your answer.

Determine whether the function $f(x)=e^x+e^{-x}$ is odd, even, or neither. Justify your answer.

Determine whether the function $f(x)=x^2-x^4-\cos (x)\sin (x)$ is odd, even, or neither. Justify your answer.

Determine whether the function $f(x)=x^3$ is odd, even, or neither. Justify your answer.

Determine whether the function $f(x)=x^2\sin (x)$ is odd, even, or neither. Justify your answer.

Determine whether the function $f(x)=x^5+x^2$ is odd, even, or neither. Justify your answer.

Determine whether the function $f(x)=\tan (x)$ is odd, even, or neither. Justify your answer.

Determine whether the function $f(x)=\frac{x^2-1}{x}$ is odd, even, or neither. Justify your answer.

Determine whether the function $f(x)=\frac{x}{1+x^2}$ is odd, even, or neither. Justify your answer.