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Chapter 1: Problem 18
Find the zeros of the function algebraically. $$f(x)=\frac{x^{2}-9 x+14}{4 x}$$
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Determine whether the statement is true or false. Justify your answer. Every function is a relation.
The median sale prices \(p\) (in thousands of dollars) of an existing one-family home in the United States from 2000 through 2010 (see figure) can be approximated by the model \(p(t)=\left\\{\begin{array}{ll}0.438 t^{2}+10.81 t+145.9, & 0 \leq t \leq 6 \\ 5.575 t^{2}-110.67 t+720.8, & 7 \leq t \leq 10\end{array}\right.\) where \(t\) represents the year, with \(t=0\) corresponding to \(2000 .\) Use this model to find the median sale price of an existing one-family home in each year from 2000 through \(2010 .\) (Source: National Association of Realtors) (GRAPH CAN'T COPY)
Find a mathematical model that represents the statement. (Determine the constant of proportionality.) \(P\) varies directly as \(x\) and inversely as the square of \(y .\) \(\left(P=\frac{28}{3} \text { when } x=42 \text { and } y=9 .\right)\)
Evaluate the function for the indicated values. \(h(x)=[x+3]\) (a) \(h(-2)\) (b) \(h\left(\frac{1}{2}\right)\) (c) \(h(4.2)\) (d) \(h(-21.6)\)
Match the data with one of the following functions $$f(x)=c x, g(x)=c x^{2}, h(x)=c \sqrt{|x|}, \quad \text {and} \quad r(x)=\frac{c}{x}$$ and determine the value of the constant \(c\) that will make the function fit the data in the table. $$\begin{array}{|c|c|c|c|c|c|}\hline x & -4 & -1 & 0 & 1 & 4 \\\\\hline y & -1 & -\frac{1}{4} & 0 & \frac{1}{4} & 1 \\\\\hline\end{array}$$
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