91Ó°ÊÓ

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. $$f(x)=\frac{1}{2} x+3$$

Assume that \(f\) is a one-to-one function. (a) If \(f(2)=7,\) find \(f^{-1}(7)\) (b) If \(f^{-1}(3)=-1,\) find \(f(-1)\)

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. $$g(x)=-4 x+2$$

Sketch the graph of the function, not by plotting points, but by starting with the graph of a standard function and applying transformations. $$f(x)=x^{2}+5$$

Assume that \(f\) is a one-to-one function. (a) If \(f(5)=18,\) find \(f^{-1}(18)\) (b) If \(f^{-1}(4)=2,\) find \(f(2)\)

Evaluate the function at the indicated values. $$\begin{aligned} &h(t)=t+\frac{1}{t} ; \\ &h(1), h(-1), h(2), h\left(\frac{1}{2}\right), h(x), h\left(\frac{1}{x}\right) \end{aligned}$$

Use \(f(x)=3 x-5\) and \(g(x)=2-x^{2}\) to evaluate the expression. (a) \(f(f(4))\) (b) \(g(g(3))\)

A function \(f\) is given. (a) Use a graphing device to draw the graph of \(f .\) (b) State approximately the intervals on which \(f\) is increasing and on which \(f\) is decreasing. $$f(x)=x^{2}-5 x$$

Use \(f(x)=3 x-5\) and \(g(x)=2-x^{2}\) to evaluate the expression. (a) \((f \circ g)(-2)\) (b) \((g \circ f)(-2)\)

Sketch the graph of the function, not by plotting points, but by starting with the graph of a standard function and applying transformations. $$f(x)=\sqrt{x}+1$$