Question

4 function ( j ) gives the temperature, in degrees celsius, ( t ) hours after midnight. use function notation to write an equation or expression for each statement.
a. the temperature at 12 p.m.
b. the temperature was the same at 9 a.m. and at 4 p.m.
c. it was warmer at 9 a.m. than at 6 a.m.
d. some time after midnight, the temperature was 24 degrees celsius.

1. write three statements that are true about this situation. use function notation.

the graph of function ( j ) shows the distance of a dog from a post, in feet, as a function of time, ( t ), in seconds, (image in corner left).
use the ( = ) sign in at least one statement and the ( < ) sign in another statement.

Explanation:

Part 4

a. The temperature at 12 p.m.

Step1: Determine hours after midnight

12 p.m. is 12 hours after midnight, so \( t = 12 \).

Step2: Write function notation

The function \( J(t) \) gives the temperature at \( t \) hours after midnight. So the temperature at 12 p.m. is \( J(12) \).

Step1: Determine hours for each time

9 a.m. is 9 hours after midnight (\( t = 9 \)), 4 p.m. is 16 hours after midnight (\( t = 16 \)).

Step2: Set function values equal

Since temperatures are equal, \( J(9)=J(16) \).

Step1: Determine hours for each time

9 a.m. is \( t = 9 \), 6 a.m. is \( t = 6 \).

Step2: Use inequality for warmer (higher temperature)

Warmer means higher temperature, so \( J(9)>J(6) \).

Answer:

\( J(12) \)

b. The temperature was the same at 9 a.m. and at 4 p.m.