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Chapter 2: Problem 62
What must be done to a function's equation so that its graph is reflected about the \(y\) -axis?
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You will be developing functions that model given conditions. Describe one advantage of using \(f(x)\) rather than \(y\) in a function's equation.
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
Begin by graphing the standard cubic function, \(f(x)=x^{3} .\) Then use transformations of this graph to graph the given function. $$ g(x)=(x-2)^{3} $$
If \(f(x)=a x^{2}+b x+c\) and \(r_{1}=\frac{-b+\sqrt{b^{2}-4 a c}}{2 a}\) find \(f\left(r_{1}\right)\) without doing any algebra and explain how you arrived at your result.
Begin by graphing the absolute value function, \(f(x)=|x| .\) Then use transformations of this graph to graph the given function. $$ h(x)=-|x+3| $$
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