Question

interpreting function notation
let f(t) be the function of the outside temperature (°f) t hours after 6 a.m. explain the meaning of each statement.
be specific about what time of day it is in each one
$f(3) = 66$
$f(0) = 60$
$f(5) < f(8)$

Explanation:

For \( f(0) = 60 \)

The function \( f(t) \) represents the outside temperature \( t \) hours after 6 a.m. When \( t = 0 \), it means 0 hours after 6 a.m., which is 6 a.m. itself. So \( f(0)=60 \) means the outside temperature at 6 a.m. is \( 60^\circ\text{F} \).

Here, \( t = 3 \), so we calculate the time by adding 3 hours to 6 a.m. 6 a.m. + 3 hours = 9 a.m. The function value \( f(3) = 66 \) means the outside temperature at 9 a.m. is \( 66^\circ\text{F} \).

First, find the times for \( t = 5 \) and \( t = 8 \). For \( t = 5 \), 6 a.m. + 5 hours = 11 a.m. For \( t = 8 \), 6 a.m. + 8 hours = 2 p.m. The inequality \( f(5) < f(8) \) means the outside temperature at 11 a.m. (5 hours after 6 a.m.) is less than the outside temperature at 2 p.m. (8 hours after 6 a.m.).

Answer:

At 6 a.m. (0 hours after 6 a.m.), the outside temperature is \( 60^\circ\text{F} \).

For \( f(3) = 66 \)