Question

3 function f gives the temperature on a certain day, in degrees celsius, t hours after midnight. use function notation to write an equation, inequality, or expression for each statement. a. the temperature at 12 pm b. the temperature was the same at 9 am and at 4 pm c. it was warmer at 9 am than at 6 am d. at t hours after midnight, the temperature was 24 °c 4 select all points that must be on the graph of f if we know that f(2) = -4 and f(5) = 3.4. a (-4, 2) b (2, -4) c (3.4, 5) d (5, 3.4) e (2, 5) 5 the graph of the function f gives the distance of a dog from a post, in feet, as a function of time, t, in seconds, since its owner left. graph: y - axis: distance from post in feet (1 - 6), x - axis: time in seconds (0 - 160). curve starts at (0, ~1.5), rises to ~3 at 20, dips to ~2.5 at 40, rises to ~5 at 60, dips to ~2 at 100, rises to ~4 at 160. a dot at (60, 4). write three statements that are true about this situation. use function notation. use the symbol = in at least one statement and the symbol < in another statement.

Explanation:

Question 3

Part a

Step1: Determine hours after midnight

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

Step2: Write function notation

The temperature at \( t = 12 \) is given by \( f(12) \).

Step1: Convert times to hours after midnight

9 am is 9 hours after midnight (\( t = 9 \)), 4 pm is 16 hours after midnight (\( t = 16 \)).

Step2: Set temperatures equal

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

Step1: Convert times to hours after midnight

9 am is \( t = 9 \), 6 am is \( t = 6 \).

Step2: Write inequality for warmer (higher temperature)

Warmer at 9 am means \( f(9)>f(6) \).

Answer:

\( f(12) \)

Part b