91Ó°ÊÓ

Express the given function \(h\) as \(a\) composition of two functions \(f\) and \(g\) so that \(h(x)=(f \circ g)(x)\). $$h(x)=|3 x-4|$$

Begin by graphing the absolute value function, \(f(x)=|x|.\) Then use transformations of this graph to graph the given function. $$g(x)=|x|+4$$

Graph each linear function. $$ 3 x-4 f(x)-6=0 $$

Explaining the Concepts Does \((x-3)^{2}+(y-5)^{2}=-25\) represent the equation of a circle? What sort of set is the graph of this equation?

Express the given function \(h\) as \(a\) composition of two functions \(f\) and \(g\) so that \(h(x)=(f \circ g)(x)\). $$h(x)=\frac{1}{2 x-3}$$

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

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). $$ f(x)=|x-2| $$

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). $$ f(x)=(x-1)^{3} $$

Begin by graphing the absolute value function, \(f(x)=|x|.\) Then use transformations of this graph to graph the given function. $$g(x)=|x|+3$$

Express the given function \(h\) as \(a\) composition of two functions \(f\) and \(g\) so that \(h(x)=(f \circ g)(x)\). $$h(x)=\frac{1}{4 x+5}$$