Q. 64 - Precalculus Enhanced with Graphing Utilities

Question

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

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

Step-by-Step Solution

Answer

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

Step 1. Given information.

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

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

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

For the point (0, 0): $y=x^3-2\sqrt{x}\Rightarrow 0=0^3-2\sqrt{0}\Rightarrow 0=0$

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

For the point (1, 1): 

$y=x^3-2\sqrt{x}\Rightarrow 1=1^3-2\sqrt{1}\Rightarrow 1\ne 1-\sqrt{2}$

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

For the point (1, -1):

$y=x^3-2\sqrt{x}\Rightarrow -1=1^3-2\sqrt{1}\Rightarrow -1=-1$

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

Step 3. Conclusion.

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