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Chapter 2: Problem 71
Determine whether each function is even, odd, or neither. $$f(x)=x \sqrt{1-x^{2}}$$
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a. Use a graphing utility to graph \(f(x)=x^{2}+1\)
b. Graph \(f(x)=x^{2}+1,\) and \(g(x)=f\left(\frac{1}{2} x\right),\) and
\(h(x)=f\left(\frac{1}{4} x\right)\) in the same viewing rectangle.
c. Describe the relationship among the graphs of \(f, g,\) and \(h,\) with
emphasis on different values of \(x\) for points on all three 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 \(0
Find a linear equation in slope-intercept form that models the given description. Describe what each variable in your model represents. Then use the model to make a prediction. In \(1995,60 \%\) of U.S. adults read a newspaper and this percentage has decreased at a rate of \(0.7 \%\) per year since then.
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? $$ y=f(x)-3 $$
Begin by graphing the standard cubic function, \(f(x)=x^{3} .\) Then use transformations of this graph to graph the given function. $$ h(x)=\frac{1}{4} x^{3} $$
Begin by graphing the standard quadratic function, \(f(x)=x^{2} .\) Then use transformations of this graph to graph the given function. $$ h(x)=(x-1)^{2}+2 $$
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