Remember the basic transformations investigated in this activity apply to all basic functions. Apply what you have learned in this lab about transformations. Write the equation of a function that has been transformed in the following ways. Write equations in $f(x)=$ form. After writing an equation check your answer using a graphing program and graph below. Be sure to label a point on the graph. Does your graph match the description?

$($a$)$ Begin with a basic square root function. Reflect the graph over the $x-$axis and shift it to the right $2$ units and down $1$ unit.

$f(x)=$

$($b$)$ Begin with an absolute value function. Stretch the graph vertically by a factor of $3$ and shift it left $4$ units and up $5$ units.

$f(x)=$