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Chapter 2: Problem 10
Find the coordinates of the vertex for the parabola defined by the given quadratic function. $$f(x)=-3(x-2)^{2}+12$$
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Determine whether each statement makes sense or does not make sense, and explain your reasoning. When solving \(f(x)>0,\) where \(f\) is a polynomial function, I only pay attention to the sign of \(f\) at each test value and not the actual function value.
You invested \(\$ 20,000\) in two accounts paying \(7 \%\) and \(9 \%\) annual interest. If the total interest earned for the year is \(\$ 1550,\) how much was invested at each rate? (Section P.8, Example 5 )
Find the domain of \(h(x)=\sqrt{36-2 x}\).
a. Find the slant asymptote of the graph of each rational function and \(\mathbf{b} .\) Follow the seven-step strategy and use the slant asymptote to graph each rational function. $$f(x)=\frac{x^{3}-1}{x^{2}-9}$$
Write the equation of a rational function \(f(x)=\frac{p(x)}{q(x)}\) having the indicated properties, in which the degrees of p and q are as small as possible. More than one correct function may be possible. Graph your function using a graphing utility to verify that it has the required properties. \(f\) has a vertical asymptote given by \(x=1,\) a slant asymptote whose equation is \(y=x, y\) -intercept at \(2,\) and \(x\)-intercepts at -1 and 2.
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