Q. 66 - Precalculus Enhanced with Graphing Utilities

Question

Tell whether the given points are on the graph of the equation.

$$\begin{gathered} \mathrm{Equation}: {\mathrm{y}}^3=\mathrm{x}+1 \\ \mathrm{Points}: (1,2); (0,1); (-1,0) \end{gathered}$$

Step-by-Step Solution

Answer

The point (-1, 0) and (0, 1) is on the graph.

Step 1. Given information.

Tell whether the given points are on the graph of the equation.

$$\begin{gathered} \mathrm{Equation}: {\mathrm{y}}^3=\mathrm{x}+1 \\ \mathrm{Points}: (1,2); (0,1); (-1,0) \end{gathered}$$

Step 2. Substitute the points in the equation to satisfy the equation.

For the point (-1, 0):

$y^3=x+1\Rightarrow 0^3=-1+1\Rightarrow 0=0$

The equation is satisfied, so the point (-1,0) is on the graph. 

For the point (0, 1):

$y^3=x+1\Rightarrow 1^3=0+1\Rightarrow 1=1$

The equation is satisfied, so the point (0,1) is on the graph. 

For the point (1, 2):

$y^3=x+1\Rightarrow 2^3=1+1\Rightarrow 8\ne 2$

The equation is not satisfied, so the point (1, 2) is not on the graph.

Step 3. Conclusion.

The point (-1, 0) and (0, 1) is on the graph.