Apply the transformations on the graph of $p(x)=\sqrt{x}$ into the graph of $h(x)=4\sqrt{x-3}-6$ . Check your work with the help of a graphing calculator.

Write the new equation after shifting the given graph as stated below. Also, plot both graphs using the same rectangular coordinate system.

$y=\frac13(x-5)+2$ Down $2$ units, right $3$ units

Determine $(uov)(x)$ and $(v o u) (x)$ for the following $u(x)$ and $v(x)$.

$u(x)=x^7$

$v(x)=x^4-6$

Consider the functions $f_1\left(x\right)=\frac{1}{2}{x}^3$ and $f_2\left(x\right)=\mid \frac{1}{2}{x}^3\mid$. Graph them together and describe how applying the absolute value function in $f_2$ modifies the graph of $f_1$.

Using the defined functions $p\left(x\right)=x^2-1$ and , evaluate $q\left(p\left(1\right)\right)$.

Solve the equation $9^{x-5}=102$ for $x$.

For the given expression, simplify.

$e^{x^2\ln (5x^2+7)}$

Determine the inverse of the function and its domain: $g\left(x\right)=\left(x-2\right)^3$