A graph has been transformed from an original function according to the following transformations. Select all of the transformations that affect the input of the function:

Each of the graphs have been transformed from the original function \(y=\sqrt{x}\). Match each graph with the transformation that was applied.

Mai solved the equation \(\sqrt[3]{x-1} +3 = 4\) and got \(x=38\).

1. Check Mai’s answer: Is the equation true if \(x=38\)? Explain or show your reasoning.
2. Here are the steps Mai took. What was her mistake?
   \(\begin{align} \sqrt[3]{x-1}+3 &= 4 \\ x - 1 + 27 &= 64 \\ x + 26 &= 64 \\ x &= 38 \\ \end{align}\)
3. Solve the equation \(\sqrt[3]{x-1} +3 = 4\).

For each exponential equation, write an equivalent equation in logarithmic form.

1. \(e^x = 7\)
2. \(e^2 = y\)
3. \(e^{\text-3} = \frac{1}{e^3}\)
4. \(e^\frac12 = m\)