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Unformatted text preview: s t, not x. In this context, t is chosen because it
represents time. The second is that the function is broken up into two rules: one formula for values
of t between 0 and 20 inclusive, and another for values of t greater than 20. To ﬁnd h(10), we ﬁrst
notice that 10 is between 0 and 20 so we use the ﬁrst formula listed: h(t) = −5t2 + 100t. Hence,
h(10) = −5(10)2 + 100(10) = 500. In terms of the model rocket, this means that 10 seconds after
lift oﬀ, the model rocket is 500 feet above the ground. To ﬁnd h(60), we note that 60 is greater
than 20, so we use the rule h(t) = 0. This function returns a value of 0 regardless of what value is
substituted in for t, so h(60) = 0. This means that 60 seconds after lift oﬀ, the rocket is 0 feet above
the ground; in other words, a minute after lift oﬀ, the rocket has already returned to earth.
The type of function in the previous example is called a piecewise-deﬁned function, or ‘piecewise’
function for short. Many real-world phenomena (e.g. postal rat...
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