Question

1. reinforce sketch the graph of ( y = sqrt { x } ). then sketch the graphs of ( y = sqrt { 100 x } ), ( y = sqrt { - 100 x } ), and ( y = - sqrt { 100 x } ) and describe the transformations.

Explanation:

Step1: Analyze \(y = \sqrt{100x}\)

For the function \(y=\sqrt{100x}\), we can rewrite it as \(y = 10\sqrt{x}\). This is a horizontal compression of \(y=\sqrt{x}\) by a factor of \(\frac{1}{100}\) (or a vertical stretch by a factor of \(10\)).

Step2: Analyze \(y=\sqrt{- 100x}\)

For the function \(y=\sqrt{-100x}\), we first note that the domain is \(x\leq0\). If we let \(u=-100x\), then \(y = \sqrt{u}\). This is a reflection of \(y=\sqrt{100x}\) across the \(y -\)axis.

Step3: Analyze \(y=-\sqrt{100x}\)

For the function \(y =-\sqrt{100x}\), this is a reflection of \(y=\sqrt{100x}\) across the \(x -\)axis.

Answer:

• \(y = \sqrt{100x}\): Horizontal compression (or vertical stretch) of \(y=\sqrt{x}\).
• \(y=\sqrt{-100x}\): Reflection of \(y = \sqrt{100x}\) across the \(y -\)axis.
• \(y=-\sqrt{100x}\): Reflection of \(y=\sqrt{100x}\) across the \(x -\)axis.