Input and Output [2.1]
A function is like a vending machine...
After you put in your money...
- You press a button (input),
- which *uniquely* determines what drink will come out (output).
Photo: Danial Pisano
Basic Concepts
Example 1 (formula)
Suppose $$h(t)=t^2-6/t-2.$$ [WA]
- Find $h(3)$.
- Find $h(-1)$.
- Find $h(2)$.
- Find $h(x+1)$.
- Find all $t$ that satisfy $h(t)=5$.
Example 2 (table)
The table shows the revenue, $R(t)$, received by the National Football League, NFL, from network television, as a function of the year, $t$, since 1975.
- Evaluate and interpret $R(5)$.
- Solve and interpret $R(t)=2200$.
Example 3 (in words)
Let $f(d)$ be the total number of reported cases of the flu in Indiana by the $d$-th day of the year.
- Interpret $f(103)=567$.
- Interpret $f(147)$.
- What can you say about the relationship between $f(103)$ and $f(147)$?
- Interpret $f(t)=700$.
Example 4 (graph)
A man drives from his home to a store and back. The entire trip takes 30 minutes. The graph gives his velocity, $v(t)$ (in mph) as a function of the time, $t$ (in minutes), since he left home. A negative velocity indicates that he is traveling away from the store and back to his home.
- Evaluate and interpret $v(22)$.
- Solve and interpret $v(t)=25$.
- When is the car stopped?
- How long is the man in the store?
- When was the man going the fastest?
- What was the man's fastest acceleration?