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Chapter 3: Problem 48
Give the domain and the range of each quadratic function whose graph is described. Minimum \(=18\) at \(x=-6\)
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Use point plotting to graph \(f(x)=2^{x}.\)Begin by setting up a partial table of coordinates, selecting integers from -3 to 3, inclusive, for x. Because y = 0 is a horizontal asymptote, your graph should approach, but never touch, the negative portion of the x-axis.
Use long division to rewrite the equation for \(g\) in the form $$ \text {quotient}+\frac{\text {remainder}}{\text {divisor}} $$ Then use this form of the function's equation and transformations \( \text { of } f(x)=\frac{1}{x} \text { to graph } g \). $$ g(x)=\frac{3 x+7}{x+2} $$
In Exercises 94鈥�97, use a graphing utility with a viewing rectangle large enough to show end behavior to graph each polynomial function. $$f(x)=-x^{5}+5 x^{4}-6 x^{3}+2 x+20$$
The equation for \(f\) is given by the simplified expression that results after performing the indicated operation. Write the equation for \(f\) and then graph the function. $$ \frac{1-\frac{3}{x+2}}{1+\frac{1}{x-2}} $$
Write the equation of a rational function$$ f(x)=\frac{p(x)}{q(x)} \text {having the indicated properties in which the degrees} $$ of p and q are as small as possible. More than one correct function may be possible. Graph your function using a graphing utility to verify that it has the required properties. f has a vertical asymptote given by x=1, a slant asymptote whose equation is y=x, y -intercept at 2, and x -intercepts at -1 and 2.
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