Unformatted text preview: ating the importance of ﬁnding the domain of a function before simplifying, as
evidenced by the function I in the previous example. Even though the formula I (x) simpliﬁes to
3x, it would be inaccurate to write I (x) = 3x without adding the stipulation that x = 0. It would
be analogous to not reporting taxable income or some other sin of omission.
3 The ‘radicand’ is the expression ‘inside’ the radical.
More precisely, the fraction 0 is an ‘indeterminant form’. Much time will be spent in Calculus wrestling with
4 1.5 Function Notation 49 Our next example shows how a function can be used to model real-world phenomena.
Example 1.5.4. The height h in feet of a model rocket above the ground t seconds after lift oﬀ is
h(t) = −5t2 + 100t, if 0 ≤ t ≤ 20
0, if t > 20 Find and interpret h(10) and h(60).
Solution. There are a few qualities of h which may be oﬀ-putting. The ﬁrst is that, unlike
previous examples, the independent variable i...
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