91Ó°ÊÓ

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

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. $$ f(x)=\frac{1}{x}+2, g(x)=\frac{1}{x-2} $$

Begin by graphing the absolute value function, \(f(x)=|x|.\) Then use transformations of this graph to graph the given function. $$h(x)=|x+4|-2$$

Use a graphing utility to graph each circle whoseequation is given. Use a square setting for the viewing window. $$x^{2}+10 x+y^{2}-4 y-20=0$$

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

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. $$ f(x)=\sqrt[3]{x}-2, g(x)=(x+2)^{3} $$

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

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I’ve noticed that in mathematics, one topic often leads logically to a new topic:

Determine whether each statement makes sense or does not make sense, and explain your reasoning. To avoid sign errors when finding h and k, I place parentheses around the numbers that follow the subtraction signs in a circle’s equation.

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