91Ó°ÊÓ

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). $$ f(x)=\frac{x^{4}}{4} $$

Express the given function \(h\) as \(a\) composition of two functions \(f\) and \(g\) so that \(h(x)=(f \circ g)(x)\). $$h(x)=|2 x-5|$$

find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$ for the given function. $$ f(x)=2 x^{2}+x-1 $$

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

How is the standard form of a circle’s equation obtained from its general form?

Find the value of \(y\) if the line through the two given points is to have the indicated slope. $$ (-2, y) \text { and }(4,-4), m=\frac{1}{3} $$

find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$ for the given function. $$ f(x)=3 x^{2}+x+5 $$

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). $$ f(x)=\operatorname{int}(x-2) $$

Does \((x-3)^{2}+(y-5)^{2}=0\) represent the equation of a circle? If not, describe the graph of this equation.

Begin by graphing the square root function, \(f(x)=\sqrt{x}.\) Then use transformations of this graph to graph the given function. $$g(x)=2 \sqrt{x+1}-1$$