Question

u4: warm-up #26: interpreting & using function notation
function f gives the temperature, in degrees celsius, t hours after midnight.
choose the equation that represents the statement: \at 1:30 p.m., the temperature was 20 degrees celsius.\
○ f(13:30) = 20
○ f(1:30) = 20
○ f(13.5) = 20
○ f(1.5) = 20

Explanation:

Step1: Understand Function Notation

Function \( f(t) \) takes \( t \) (hours after midnight) as input and gives temperature. So \( t \) must be in hours (numerical, not time format like \( 13:30 \) or \( 1:30 \)).

Step2: Convert 1:30 p.m. to Hours After Midnight

1:30 p.m. is 13.5 hours after midnight (12 + 1.5 = 13.5).

Step3: Evaluate Options

• \( f(13:30) \): Invalid, \( t \) should be numerical (hours), not time string.
• \( f(1:30) \): Invalid, same as above, time string not numerical hours.
• \( f(13.5) = 20 \): 13.5 hours after midnight is 1:30 p.m., so this represents temperature at 1:30 p.m. being 20.
• \( f(1.5) = 20 \): 1.5 hours after midnight is 1:30 a.m., not p.m.

Answer:

\( f(13.5) = 20 \) (the third option)