Input and Output [2.1]

• A function can be represented with a formula, a table, words, or a graph.
• For a particular input, find the unique output of a function.
• For a particular output of a function, find the possible inputs.
• Input $\Leftrightarrow$ Independent Variable $\Leftrightarrow$ Horizontal Axis $\Leftrightarrow$ Top Row
• Output $\Leftrightarrow$ Dependent Variable $\Leftrightarrow$ Vertical Axis $\Leftrightarrow$ Bottom Row

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?