Question

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

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

Short answer

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

Step-by-step solution

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):

localid="1645796714834" $y=x^3-2\sqrt{x}\Rightarrow -1=1^3-2\sqrt{1}\Rightarrow -1=-1$

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.