91Ó°ÊÓ

Find \(f(a), f(a+h),\) and the difference quotient \(\frac{f(a+h)-f(a)}{h},\) where \(h \neq 0\). $$f(x)=3 x+2$$

A linear function is given. (a) Find the average rate of change of the function between \(x=a\) and \(x=a+h\) (b) Show that the average rate of change is the same as the slope of the line. $$f(x)=\frac{1}{2} x+3$$

29–38 Find the maximum or minimum value of the function. $$f(x)=x^{2}+x+1$$

A function \(f\) is given. (a) Use a graphing calculator to draw the graph of \(f\) (b) Find the domain and range of \(f\) from the graph. $$f(x)=4$$

Use the Inverse Function Property to show that f and g are inverses of each other. $$\begin{aligned}&f(x)=\frac{1}{x-1}, \quad x \neq 1\\\&g(x)=\frac{1}{x}+1, \quad x \neq 0\end{aligned}$$

A function \(f\) is given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final transformed graph. \(f(x)=\sqrt[3]{x} ;\) reflect in the \(y\) -axis, shrink vertically by a factor of \(\frac{1}{2},\) and shift upward \(\frac{3}{5}\) unit

A linear function is given. (a) Find the average rate of change of the function between \(x=a\) and \(x=a+h\) (b) Show that the average rate of change is the same as the slope of the line. $$g(x)=-4 x+2$$

Find \(f(a), f(a+h),\) and the difference quotient \(\frac{f(a+h)-f(a)}{h},\) where \(h \neq 0\). $$f(x)=x^{2}+1$$

A function \(f\) is given. (a) Use a graphing calculator to draw the graph of \(f\) (b) Find the domain and range of \(f\) from the graph. $$f(x)=-x^{2}$$

Find the functions \(f \circ g, g \circ f, f \circ f,\) and \(g \circ g\) and their domains. $$f(x)=6 x-5, \quad g(x)=\frac{x}{2}$$