91Ó°ÊÓ

Geometry You toss a pebble into a pool of water and watch the circular ripples radiate outward. You find that the function \(r(x)=12.5 x\) describe the radius \(r\) in inches of a circle \(x\) seconds after it was formed. The function \(A(x)=\pi x^{2}\) describes the area \(A\) of a circle with radius \(x .\) a. Find \((A \circ r)(x)\) when \(x=2 .\) Interpret your answer. b. Find the area of a circle 4 seconds after it was formed.

Explain the effect that \(a\) has on the graph of \(y=a \sqrt{x}\)

What is the inverse of \(y=x^{2}-3 ?\) $$ \begin{array}{ll}{\text { A. } y=\pm \sqrt{x}+3} & {\text { B. } y=\pm \sqrt{x}-3} \\ {\text { C. } y=\pm \sqrt{x+3}} & {\text { D. } y=\pm \sqrt{x-3}}\end{array} $$

Solve each equation. $$ 2 x^{3}-16=0 $$

Writing A salesperson earns a 3\(\%\) bonus on weekly sales over \(\$ 5000\) . $$\begin{array}{l}{g(x)=0.03 x} \\ {h(x)=x-5000}\end{array}$$ a. Explain what each function above represents. b. Which composition, \((h \circ g)(x)\) or \((g \circ h)(x),\) represents the weekly bonus? Explain.

Simplify each expression. Assume that all variables are positive. $$\left(\frac{81 y^{16}}{16 x^{12}}\right)^{\frac{1}{2}}$$

The graph of \(y=-\sqrt{x}\) is shifted 4 units up and 3 units right. Which equation represents the new graph? A. \(y=-\sqrt{x-4}+3\) B. \(y=-\sqrt{x-3}+4\) C. \(y=-\sqrt{x+3}+4\) D. \(y=-\sqrt{x+4}+3\)

Rewrite each equation in vertex form. $$ y=-2 x^{2}+x-10 $$

Divide. Tell whether each divisor is a factor of the dividend. $$ \left(x^{3}+27\right) \div(x+3) $$

Exponents that are irrational numbers can be defined so that all the properties of rational exponents are also true for irrational exponents. Use those properties to simplify each expression. $$\left(3^{2+\sqrt{2}}\right)^{2-\sqrt{2}}$$