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Chapter 1: Problem 5
Plot the given point in a rectangular coordinate system. $$(-3,-5)$$
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Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$for the given function. $$f(x)=\sqrt{x-1}$$
Use a graphing utility to graph each circle whose equation is given. Use a square setting for the viewing window. $$(y+1)^{2}=36-(x-3)^{2}$$
Write the standard form of the equation of the circle with the given center and radius. $$x^{2}+(y-2)^{2}=4$$
a. Graph the functions \(f(x)=x^{n}\) for \(n=2,4,\) and 6 in a [-2,2,1] by [-1,3,1] viewing rectangle. b. Graph the functions \(f(x)=x^{n}\) for \(n=1,3,\) and 5 in a [-2,2,1] by [-2,2,1] viewing rectangle. c. If \(n\) is positive and even, where is the graph of \(f(x)=x^{n}\) increasing and where is it decreasing? d. If \(n\) is positive and odd, what can you conclude about the graph of \(f(x)=x^{n}\) in terms of increasing or decreasing behavior? e. Graph all six functions in a [-1,3,1] by [-1,3,1] viewing rectangle. What do you observe about the graphs in terms of how flat or how steep they are?
Determine whether each statement makes sense or does not make sense, and explain your reasoning. My graph is decreasing on \((-\infty, a)\) and increasing on \((a, \infty)\) so \(f(a)\) must be a relative maximum.
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