91Ó°ÊÓ

find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$ for the given function. $$ f(x)=x^{2}-4 x+3 $$

Express the given function \(h\) as \(a\) composition of two functions \(f\) and \(g\) so that \(h(x)=(f \circ g)(x)\). $$h(x)=\sqrt[3]{x^{2}-9}$$

Begin by graphing the square root function, \(f(x)=\sqrt{x}.\) Then use transformations of this graph to graph the given function. $$h(x)=\sqrt{x+2}-2$$

What is a circle? Without using variables, describe how the definition of a circle can be used to obtain a form of its equation.

find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$ for the given function. $$ f(x)=x^{2}-5 x+8 $$

Give an example of a circle’s equation in standard form. Describe how to find the center and radius for this circle.

Begin by graphing the square root function, \(f(x)=\sqrt{x}.\) Then use transformations of this graph to graph the given function. $$h(x)=\sqrt{x+1}-1$$

Express the given function \(h\) as \(a\) composition of two functions \(f\) and \(g\) so that \(h(x)=(f \circ g)(x)\). $$h(x)=\sqrt{5 x^{2}+3}$$

Use a graphing utility to graph the function. Use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one). $$ f(x)=\frac{x^{3}}{2} $$

Find the value of \(y\) if the line through the two given points is to have the indicated slope. $$ (3, y) \text { and }(1,4), m=-3 $$