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Question
The distance of an object falling is a function of time t and can be expressed as s(t) = −16t2. Graph the function and determine if it is one-to-one.
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Solution
Given s(t) = –16t2
s(t1) = s(t2)
⇒ –16t12 = –16t22
⇒ t12 = t22
⇒ ± t1 = ± t2
Since s(t1) = s(t1)
⇒ 14t1 = t2
∴ The function s(t) is not one-one
Graph of s(t) = –16t2
Take the time along x-axis and distance along y-axis.
| t | 0 | 1 | 2 | 3 |
| s(t) | 0 | – 16 | – 64 | – 144 |
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