Question

1. function f 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.

Explanation:

Part a

Step1: Determine hours after midnight

12 p.m. is 12 hours after midnight.

Step2: Use function notation

Function \( f \) takes \( t \) (hours after midnight) as input, so temperature at 12 p.m. is \( f(12) \).

Part b

Step1: Convert times to hours after midnight

9 a.m. is 9 hours after midnight, 4 p.m. is \( 12 + 4 = 16 \) hours after midnight.

Step2: Set function values equal

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

Part c

Step1: Convert times to hours after midnight

9 a.m. is 9 hours, 6 a.m. is 6 hours after midnight.

Step2: Compare function values

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

Part d

Answer:

$f(12)$