Chapter ISG, Problem 7.3.5P

a.

To determine

To evaluate the given statement.

Answer to Problem 7.3.5P

The graph does not show $y=x^{\frac{1}{2}}$

Explanation of Solution

Given information:

Javier thinks equation $y=x^{\frac{1}{2}}$ is shown by the given graph.

Concept Used:

Graph evaluation

Graph:

  

Calculation:

The given graph does not show the equation $y=x^{\frac{1}{2}}$ , instead is a graph of $x=y^2$ .

The equation only gives positive values of “y” and the graph will be half parabola, as drawn above.

Conclusion:

No the given graph is not of equation $y=x^{\frac{1}{2}}$ .

b.

To determine

To evaluate the given statement.

Answer to Problem 7.3.5P

The graph show $y={\frac{1}{2}}^x$

Explanation of Solution

Given information:

Lara thinks equation $y={\frac{1}{2}}^x$ is shown by the given graph.

Concept Used:

Graph evaluation

Graph:

  

Calculation:

The given graph does not show the equation $y={\frac{1}{2}}^x$ .

The graph of $y={\frac{1}{2}}^x$ is equivalent to the reflection of $y=2^x$ about the y-axis.

Conclusion:

The given statement of Lara is correct.

c.

To determine

To evaluate the given statements.

Answer to Problem 7.3.5P

  $\sqrt{({\left|x\right|}^2)}=x$ Is the right equation.

Explanation of Solution

Given information:

Brad claims $\sqrt{({\left|x\right|}^2)}=x$

Rosa says $\sqrt{({\left|x\right|}^2)}=\left|x\right|$

Concept Used:

Equation solving

Calculation:

Calculating $\sqrt{({\left|x\right|}^2)}$ ,

Opening the mod,

  $\sqrt{{(\pm x)}^2}$

So,

  $\sqrt{x^2}$

On solving,

  $x$

Hence, Brad is correct with his claim

Conclusion:

  $\sqrt{({\left|x\right|}^2)}=x$ Is the right equation.