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Chapter 1: Problem 75
List the quadrant or quadrants satisfying each condition. $$x y>0$$
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Graph \(y_{1}=x^{2}-2 x, y_{2}=x,\) and \(y_{3}=y_{1} \div y_{2}\) in the same [-10,10,1] by [-10,10,1] vicwing rectangle. Then use the TRACE l feature to trace along \(y_{3}\). What happens at \(x=0 ?\) Explain why this occurs.
Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$for the given function. $$f(x)=\frac{1}{x}$$
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.
The toll to a bridge costs \(\$ 6.00 .\) Commuters who frequently use the bridge have the option of purchasing a monthly discount pass for \(\$ 30.00 .\) With the discount pass, the toll is reduced to \(\$ 4.00 .\) For how many bridge crossings per month will the cost without the discount pass be the same as the cost with the discount pass? What will be the monthly cost for each option?
Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$for the given function. $$f(x)=7$$
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