Chapter 2.4, Problem 3AYU

List the intercepts of the equation $y=x^3-8$. (pp. 18-19)

To determine

To find: Intercepts of the equation $y=x^3-8$.

Answer to Problem 3AYU

Solution:

The $x-\text{intercept}$ is 2; the $y-\text{intercepts}$ is $-8$.

Explanation of Solution

Given:

It is asked to find the intercepts of equation $y=x^3-8$.

Formula used:

Intercepts ($x$ and $y$ intercepts): The points, if any, at which a graph crosses or touches the coordinate axes are called the intercepts.

The $x-\text{coordinate}$ of a point at which the graph crosses or touches the $x-\text{axis}$ is an $x-\text{intercept}$, and the $y-\text{coordinate}$ of a point at which the graph crosses or touches the $y-\text{axis}$ is a $y-\text{intercept}$.

The intercepts of the graph are the points

$\left(0,-8\right)$ and $\left(2,0\right)$.

The $x-\text{intercept}$ is 2; the $y-\text{intercepts}$ is $-8$.