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Subsection1.4Functions Defined by Equations

Example1.10 illustrates a function defined by an equation.


As of 2016, One World Trade Center in New York City is the nations tallest building, at 1776 feet. If an algebra book is dropped from the top of One World Trade Center, its height above the ground after \(t\) seconds is given by the equation

\begin{equation*} h = 1776 - 16t^2 \end{equation*}

Thus, after \(1\) second the books height is

\begin{equation*} h = 1776 - 16(1)^2 = 1760 \text{ feet} \end{equation*}

After \(2\) seconds its height is

\begin{equation*} h = 1776 - 16(2)^2 = 1712 \text{ feet} \end{equation*}

For this function, \(t\) is the input variable and \(h\) is the output variable. For any value of \(t\text{,}\) a unique value of \(h\) can be determined from the equation for \(h\text{.}\) We say that \(h\) is a function of \(t\text{.}\)