Q. 63 - Precalculus Enhanced with Graphing Utilities

Question

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

$$\begin{gathered} \mathrm{Equation}: \mathrm{y}={\mathrm{x}}^4-\sqrt{\mathrm{x}} \\ \mathrm{Points}: (0,0); (1,1); (-1,0) \end{gathered}$$

Step-by-Step Solution

Answer

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

Step 1. Given information.

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

$$\begin{gathered} \mathrm{Equation}: \mathrm{y}={\mathrm{x}}^4-\sqrt{\mathrm{x}} \\ \mathrm{Points}: (0,0); (1,1); (-1,0) \end{gathered}$$

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

For the point (0, 0):$y={\mathrm{x}}^4-\sqrt{\mathrm{x}}\Rightarrow 0=0^4-\sqrt{0}\Rightarrow 0=0$

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

For the point (1, 1):

$y=x^4-\sqrt{x}\Rightarrow 1=1^4-\sqrt{4}\Rightarrow 1=1-2\Rightarrow 1\ne -1$

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

For the point (-1, 0):

$y=x^4-\sqrt{x}\Rightarrow -1=0^4-\sqrt{0}\Rightarrow -1\ne 0$

The equation is not satisfied, so the point (-1, 0) is not on the graph. 

Step 3. Conclusion.

The point (0,0) is on the graph.