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Chapter 2: Problem 55
Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}-2 x+y^{2}-15=0$$
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a. Use a graphing utility to graph \(f(x)=x^{2}+1\)
b. Graph \(f(x)=x^{2}+1,\) and \(g(x)=f\left(\frac{1}{2} x\right),\) 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
Begin by graphing the absolute value function, \(f(x)=|x| .\) Then use transformations of this graph to graph the given function. $$ h(x)=2|x+3| $$
Prove that the equation of a line passing through \((a, 0)\) and \((0, b)(a \neq 0, b \neq 0)\) can be written in the form \(\frac{x}{a}+\frac{y}{b}=1 .\) Why is this called the intercept form of a line?
Give an example of an equation that does not define \(y\) as a function of \(x\) but that does define \(x\) as a function of \(y .\)
Find a linear equation in slope-intercept form that models the given description. Describe what each variable in your model represents. Then use the model to make a prediction. In \(1995,\) the average temperature of Earth was \(57.7^{\circ} \mathrm{F}\) and has increased at a rate of \(0.01^{\circ} \mathrm{F}\) per year since then.
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