91Ó°ÊÓ

Use the Law of Exponents to rewrite and simplify the expression. $$ \begin{array}{lll}{\text { (a) } b^{8}(2 b)^{4}} & {\text { (b) } \frac{\left(6 y^{3}\right)^{4}}{2 y^{5}}} & {}\end{array} $$

A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one. $$ \begin{array}{|c|c|c|c|c|c|c|}\hline x & {1} & {2} & {3} & {4} & {5} & {6} \\\ \hline f(x) & {1.5} & {2.0} & {3.6} & {5.3} & {2.8} & {2.0} \\\ \hline\end{array} $$

Match each equation with its graph. Explain your choices. (Don’t use a computer or graphing calculator.) $$ \text { (a) } y=x^{2} \quad \text { (b) } y=x^{3} \quad \text { (c) } y=x^{8} $$

A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one. $$ \begin{array}{|c|c|c|c|c|c|c|}\hline x & {1} & {2} & {3} & {4} & {5} & {6} \\\ \hline f(x) & {1.0} & {1.9} & {2.8} & {3.5} & {3.1} & {2.9} \\\ \hline\end{array} $$

Match each equation with its graph. Explain your choices. (Don’t use a computer or graphing calculator.). $$ \text { (a) } y=3 x \quad \text { (b) } y=3^{x} \quad \text { (c) } y=x^{3} \quad \text { (d) } y=\sqrt[3]{x} $$

Use the Law of Exponents to rewrite and simplify the expression. $$ \text { (a) } \frac{x^{2 n} \cdot x^{3 n-1}}{x^{n+2}} \quad \text { (b) } \frac{\sqrt{a \sqrt{b}}}{\sqrt[3]{a b}} $$

(a) Write an equation that defines the exponential function with base \(b>0\). (b) What is the domain of this function? (c) If \(b \neq 1,\) what is the range of this function? (d) Sketch the general shape of the graph of the exponential function for each of the following cases. $$ \begin{array}{ll}{\text { (i) }} & {b>1} \\ {\text { (ii) }} & {b=1} \\\ {\text { (iii) }} & {0

(a) How is the number \(e\) defined? (b) What is an approximate value for \(e ?\) (c) What is the natural exponential function?

A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one.

Find the domain of the function. $$ g(x)=\frac{1}{1-\tan x} $$