91Ó°ÊÓ

For each function. \(\bullet\) Find its domain. \(\bullet\) Create a sign diagram. \(\bullet\) Use your calculator to help you sketch its graph and identify any vertical or horizontal asymptotes, 'unusual steepness' or cusps. $$f(x)=\sqrt{1-x^{2}}$$

For each function. \(\bullet\) Find its domain. \(\bullet\) Create a sign diagram. \(\bullet\) Use your calculator to help you sketch its graph and identify any vertical or horizontal asymptotes, 'unusual steepness' or cusps. $$f(x)=\frac{5 x}{\sqrt[3]{x^{3}+8}}$$

Show that the given function is one-to-one and find its inverse. Check your answers algebraically and graphically. Verify that the range of \(f\) is the domain of \(f^{-1}\) and vice-versa. $$f(x)=2-\sqrt{x-5}$$

Show that the given function is one-to-one and find its inverse. Check your answers algebraically and graphically. Verify that the range of \(f\) is the domain of \(f^{-1}\) and vice-versa. $$f(x)=3 \sqrt{x-1}-4$$

For each function. \(\bullet\) Find its domain. \(\bullet\) Create a sign diagram. \(\bullet\) Use your calculator to help you sketch its graph and identify any vertical or horizontal asymptotes, 'unusual steepness' or cusps. $$f(x)=x^{\frac{2}{3}}(x-7)^{\frac{1}{3}}$$

Show that the given function is one-to-one and find its inverse. Check your answers algebraically and graphically. Verify that the range of \(f\) is the domain of \(f^{-1}\) and vice-versa. $$f(x)=3(x+4)^{2}-5, x \leq-4$$

With help from your classmates, find the inverses of the functions in Exercises \(21-24\). $$f(x)=a x+b, a \neq 0$$

Solve the equation or inequality. $$10-\sqrt{x-2} \leq 11$$

Use \(f(x)=-2 x, g(x)=\sqrt{x}\) and \(h(x)=|x|\) to find and simplify expressions for the following functions and state the domain of each using interval notation. $$(g \circ h \circ f)(x)$$

Use \(f(x)=-2 x, g(x)=\sqrt{x}\) and \(h(x)=|x|\) to find and simplify expressions for the following functions and state the domain of each using interval notation. $$(f \circ h \circ g)(x)$$