Q. 3 - Precalculus Enhanced with Graphing Utilities

Question

List the intercepts of the equation $y=x^3-8$.

Step-by-Step Solution

Answer

The intercepts of the equation $y=x^3-8$ are $(0,-8)$ and $(2,0)$.

Step 1. Given information

We have been given an equation $y=x^3-8$.

We have to list the intercepts of this equation.

Step 2. Find the x-intercept

Put $y=0$ in the equation $y=x^3-8$.

$$\begin{gathered} 0=x^3-8 \\ {x}^3=8 \\ x=\sqrt[3]{8} \\ x=\sqrt[3]{2^3} \\ x=2 \end{gathered}$$

Therefore, the x-intercept is $(2,0)$.

Step 3. Find the y-intercept

Put $x=0$ in the equation $y=x^3-8$.

$$\begin{gathered} y=0^3-8 \\ y=0-8 \\ y=-8 \end{gathered}$$

Therefore, the y-intercept is $(0,-8)$.