91Ó°ÊÓ

Begin by graphing the standard quadratic function, \(f(x)=x^{2} .\) Then use transformations of this graph to graph the given function. $$ g(x)=(x-2)^{2} $$

Find \(f+g, f-g, f g,\) and \(\frac{f}{g}\). Determine the domain for each function. $$f(x)=2 x+3, g(x)=x-1$$

Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. $$(3,-4)\( and \)(3,5)$$

Find the midpoint of each line segment with the given endpoints. $$(10,4) \text { and }(2,6)$$

In Exercises \(33-44\), find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$for the given function. $$f(x)=6 x+1$$

Evaluate each piecewise function at the given values of the independent variable. $$h(x)=\left\\{\begin{array}{cl}\frac{x^{2}-9}{x-3} & \text { if } x \neq 3 \\\ 6 & \text { if } x=3\end{array}\right.$$ a. \(h(5)\) b. \(h(0)\) c. \(h(3)\)

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}+6 x+2 y+6=0$$

Find the average rate of change of the function from \(x_{1}\) to \(x_{2}.\) $$f(x)=3 x \text { from } x_{1}=0 \text { to } x_{2}=5$$

a. Use a graphing utility to graph \(f(x)=x^{2}+1\) b. Graph \(f(x)=x^{2}+1, g(x)=f(2 x), h(x)=f(3 x)\) and \(k(x)=f(4 x)\) in the same viewing rectangle. c. Describe the relationship among the graphs of \(f, g, h\) and \(k,\) with emphasis on different values of \(x\) for points on all four graphs that give the same \(y\) -coordinate. d. Generalize by describing the relationship between the graph of \(f\) and the graph of \(g,\) where \(g(x)=f(c x)\) for \(c>1\) e. Try out your generalization by sketching the graphs of \(f(c x)\) for \(c=1, c=2, c=3,\) and \(c=4\) for a function of your choice.

Assume that \((a, b)\) is a point on the graph of \(f .\) What is the corresponding point on the graph of each of the following functions? $$ y=f(-x) $$