Question

1 which graph models the volume of a cube with side lengths x? 2 analyze the table of values for the functions f(x) and g(x). which statement describes the function h(x)=f(x)·g(x)? a. it has no x - intercepts. b. it has one x - intercept at x = 0. c. it has x - intercepts at x=-1 and x = 1. d. it has x - intercepts at x=-1,x = 0, and x = 1.

Explanation:

Step1: Find volume formula for cube

The volume $V$ of a cube with side - length $x$ is given by $V = x^{3}$. The function $y=x^{3}$ is an odd - function, symmetric about the origin. When $x>0$, $y>0$ and when $x < 0$, $y < 0$. Graph a represents the function $y = x^{3}$.

Step2: Analyze $h(x)=f(x)\cdot g(x)$ for $x$ - intercepts

The $x$ - intercepts of a function $y = h(x)$ occur when $h(x)=0$. Since $h(x)=f(x)\cdot g(x)$, then $h(x) = 0$ when either $f(x)=0$ or $g(x)=0$. From the table, $f(x)=0$ when $x = 1$ and $g(x)=0$ when $x=-1$. So $h(x)$ has $x$ - intercepts at $x=-1$ and $x = 1$.

Answer:

1. a
2. c