The graph of which function is the same as the graph of \( y=\frac{1}{x} \) shifted to the right 5 units and shifted up 2 units? \[ y=\frac{1}{x-5}+2 \] \( y=\frac{1}{x+5}+2 \) \( y=\frac{1}{x+5}-2 \) \( y \)

\[ s(x)=(3-x)^{3} \] Step 1 of 2 : Determine the more basic function that has been shifted, reflected, stretched, or compressed. Answer \[ f(x)= \]

Consider the following piecewise-defined function. \[ f(x)=\left\{\begin{array}{ll}\frac{-5}{x+3} & \text { if } x<-3 \\ -9 & \text { if } x=-3 \\ -x^{2}+4 & \text { if } x>-3\end{array}\right. \] Step 3 of 3 : Evaluate this function at \( x=7 \). Write the exact answer. Do not round. If the answer is undefined, write Und as your answer. Answer \[ f(7)= \]

Find the gradiut of the points \( (1,6) \) and \( (2,3) \)

Find the domain of the given function and state in Interval notation. \( f(x)=\frac{\sqrt{x-1}}{x-8} \) Domain:

Use properties of logarithms to expand the logarithmic expression as much as possible. Evaluate logarithmic expressions without using a calculator if possible. \( \log _{\mathrm{b}}\left(\frac{x^{3} y}{z^{7}}\right) \)