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Chapter 1: Problem 7
Where is the tangent function undefined?
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Beginning with the graphs of \(y=\sin x\) or \(y=\cos x,\) use shifting and scaling transformations to sketch the graph of the following functions. Use a graphing utility only to check your work. $$q(x)=3.6 \cos (\pi x / 24)+2$$
Make a sketch of the given pairs of functions. Be sure to draw the graphs accurately relative to each other. $$y=x^{4} \text { and } y=x^{6}$$
Finding the inverse of a cubic polynomial is equivalent to solving a cubic equation. A special case that is simpler than the general case is the cubic \(y=f(x)=x^{3}+a x\). Find the inverse of the following cubics using the substitution (known as Vieta's substitution) \(x=z-a /(3 z) .\) Be sure to determine where the function is one-to-one. $$f(x)=x^{3}-2 x$$
Let \(E\) be an even function and O be an odd function. Determine the symmetry, if any, of the following functions. $$\boldsymbol{O} \circ \boldsymbol{E}$$
Make a sketch of the given pairs of functions. Be sure to draw the graphs accurately relative to each other. $$y=x^{3} \text { and } y=x^{7}$$
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