91Ó°ÊÓ

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$for the given function. $$f(x)=-3 x^{2}+x-1$$

Use a graphing utility to graph \(f\) and \(g\) in the same \([-8,8,1]\) by \([-5,5,1]\) viewing rectangle. In addition, graph the line \(y=x\) and visually determine if \(f\) and \(g\) are inverses. $$f(x)=\sqrt[3]{x}-2, g(x)=(x+2)^{3}$$

Begin by graphing the absolute value function, \(f(x)=|x| .\) Then use transformations of this graph to graph the given function. $$h(x)=|x+3|-2$$

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

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I found the inverse of \(f(x)=5 x-4\) in my head: The reverse of multiplying by 5 and subtracting 4 is adding 4 and dividing by \(5,\) so \(f^{-1}(x)=\frac{x+4}{5}\).

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$for the given function. $$f(x)=6$$

Will help you prepare for the material covered in the next section. Here are two sets of ordered pairs: $$\begin{array}{l}\text { set } 1:\\{(1,5),(2,5)\\} \\\\\text { set } 2:\\{(5,1),(5,2)\\}\end{array}$$ In which set is each \(x\) -coordinate paired with only one \(y\) -coordinate?

Will help you prepare for the material covered in the next section. Graph \(y=2 x\) and \(y=2 x+4\) in the same rectangular coordinate system. Select integers for \(x,\) starting with \(-2\) and ending with 2

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$for the given function. $$f(x)=7$$

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