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Chapter 2: Problem 25
Find the domain of each function. $$h(x)=\sqrt{x-2}+\sqrt{x+3}$$
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In Exercises \(105-108,\) you will be developing functions that model given conditions. A company that manufactures bicycles has a fixed cost of \(\$ 100,000 .\) It costs \(\$ 100\) to produce each bicycle. The total cost for the company is the sum of its fixed cost and variable costs. Write the total cost, \(C,\) as a function of the number of bicycles produced, \(x .\) Then find and interpret \(C(90)\)
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?
Define a piecewise function on the intervals \((-\infty, 2],(2,5)\) and \([5, \infty)\) that does not "jump" at 2 or 5 such that one piece is a constant function, another piece is an increasing function, and the third piece is a decreasing function.
give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. $$ (x+4)^{2}+(y+5)^{2}=36 $$
What is a relation? Describe what is meant by its domain and its range.
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