91Ó°ÊÓ

Write an equation for a function that has a graph with the given characteristics. The shape of \(y=|x|\), but shifted left 7 units and up 2 units

For each function \(f,\) construct and simplify the difference quotient $$ \frac{f(x+h)-f(x)}{h} $$ $$f(x)=5 x+3$$

Graph each of the following functions. Check your results using a graphing calculator. $$f(x)=\left\\{\begin{array}{ll} -\frac{1}{3} x+2, & \text { for } x \leq 0 \\ x-5, & \text { for } x>0 \end{array}\right.$$

Determine whether the function is even, odd, or neither even nor odd. $$f(x)=\frac{x^{2}+1}{x^{3}-1}$$

Write an equation for a function that has a graph with the given characteristics. The shape of \(y=x^{3},\) but reflected across the \(x\) -axis and shifted right 5 units

A blouse that is size \(x\) in Japan is size \(s(x)\) in the United States, where \(s(x)=x-3 . \mathrm{A}\) blouse that is size \(x\) in the United States is size \(t(x)\) in Australia, where \(t(x)=x+4 .\) (Source: www. onlineconversion.com) Find a function that will convert blouse sizes in Japan to blouse sizes in Australia. (IMAGE CANNOT COPY)

Write an equation for a function that has a graph with the given characteristics. The shape of \(y=1 / x,\) but shrunk horizontally by a factor of 2 and shifted down 3 units

For each function \(f,\) construct and simplify the difference quotient $$ \frac{f(x+h)-f(x)}{h} $$ $$f(x)=5 x+3$$

Graph each of the following functions. Check your results using a graphing calculator. $$f(x)=\left\\{\begin{array}{ll} -\frac{3}{4} x+2, & \text { for } x<4 \\ -1, & \text { for } x \geq 4 \end{array}\right.$$

Write an equation for a function that has a graph with the given characteristics. The shape of \(y=x^{2},\) but shifted right 6 units and up 2 units