decide whether the following statement is true or false. the cube function is odd and is increasing on the…

decide whether the following statement is true or false. the cube function is odd and is increasing on the interval (-∞,∞). choose the correct answer below. false true

decide whether the following statement is true or false. the cube function is odd and is increasing on the interval (-∞,∞). choose the correct answer below. false true

Answer

Explanation:

Step1: Define the cube function

The cube function is $y = f(x)=x^{3}$.

Step2: Check if it's odd

We need to check if $f(-x)=-f(x)$. Substitute $-x$ into $f(x)$: $f(-x)=(-x)^{3}=-x^{3}=-f(x)$. So it's odd.

Step3: Check its increasing - property

Take the derivative of $y = x^{3}$, $y'=3x^{2}$. Since $y' = 3x^{2}\geq0$ for all $x\in(-\infty,\infty)$ and $y' = 0$ only at $x = 0$ (a single - point), the function is increasing on $(-\infty,\infty)$.

Answer:

True