91Ó°ÊÓ

a. Use a graphing utility to graph \(f(x)=x^{2}+1\) b. Graph \(f(x)=x^{2}+1, g(x)=f\left(\frac{1}{2} x\right),\) 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

I noticed that the difference quotient is always zero if \(f(x)=c,\) where \(c\) is any constant.

During the winter, you program your home thermostat so that at midnight, the temperature is \(55^{\circ} .\) This temperature is maintained until 6 a. \(M\). Then the house begins to warm up so that by 9 A.M. the temperature is \(65^{\circ} .\) At 6 P.M. the house begins to cool. By 9 P.M., the temperature is again \(55^{\circ}\). The graph illustrates home temperature, \(f(t),\) as a function of hours after midnight, \(t\). (Graph can't copy) Using the graph at the bottom of the previous column, determine whether each statement makes sense or does not make sense, and explain your reasoning. If the statement makes sense, graph the new function on the domain \([0,24] .\) If the statement does not make sense, correct the function in the statement and graph the corrected function on the domain [0,24] I decided to keep the house \(5^{\circ}\) warmer than before, so I reprogrammed the thermostat to \(y=f(t)+5\)

Sketch the graph of \(f\) using the following properties. (More than one correct graph is possible.) \(f\) is a piecewise function that is decreasing on \((-\infty, 2), f(2)=0, f\) is increasing on \((2, \infty),\) and the range of \(f\) is \([0, \infty)\)