91Ó°ÊÓ

In Exercises \(1-10,\) 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. $$ (5,3) \text { and }(5,-2) $$

In Exercises 1–30, find the domain of each function. $$ g(x)=\frac{1}{\sqrt{x+2}} $$

The bar graph shows that as costs changed over the decades, Americans devoted less of their budget to groceries and more to health care. (Graph can't copy) Find a linear function in slope-intercept form that models the given description. Each function should model the percentage of total spending, \(p(x),\) by A mericans \(x\) years after 1950 . In \(1950,\) Americans spent \(3 \%\) of their budget on health care. This has increased at an average rate of approximately \(0.22 \%\) per year since then.

Graph the given square root functions, \(f\) and \(g\) in the same rectangular coordinate system. Use the integer values of x given to the right of each function to obtain ordered pairs. Because only non negative numbers have square roots that are real numbers, be sure that each graph appears only for values of \(x\) that cause the expression under the radical sign to be greater than or equal to zero. Once you have obtained your graphs, describe how the graph of \(g\) is related to the graph of \(f\) $$\begin{array}{l} f(x)=\sqrt{x} \quad(x=0,1,4,9) \text { and } \\ g(x)=\sqrt{x}-1 \quad(x=0,1,4,9) \end{array}$$

In Exercises \(59-70,\) the domain of each piecewise function is \((-\infty, \infty)\) a. Graph each function. b. Use your graph to determine the function's range. $$ f(x)=\left\\{\begin{array}{rll} {-x} & {\text { if }} & {x<0} \\ {x} & {\text { if }} & {x \geq 0} \end{array}\right. $$

In your own words, describe how to find the distance between two points in the rectangular coordinate system.

Begin by graphing the square root function, \(f(x)=\sqrt{x}.\) Then use transformations of this graph to graph the given function. $$g(x)=2 \sqrt{x+2}-2$$

How is the standard form of a circle’s equation obtained from its general form?

Express the given function \(h\) as \(a\) composition of two functions \(f\) and \(g\) so that \(h(x)=(f \circ g)(x)\). $$h(x)=\frac{1}{4 x+5}$$

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