Final answer:
Johan climbs stairs at a rate of 3 stairs per second. The function representing the stairs he has left after x seconds is f(x) = 24 - 3x. After 5 seconds, he will have 9 stairs left (f(5) = 9), and it will take him 2 seconds to have 18 stairs left (f(x) = 18 when x = 2).
Step-by-step explanation:
Understanding the Stair Climbing Function
To represent Johan's stair climbing in function notation after x seconds, we begin by expressing the total stairs to climb, which is 24. Johan climbs 3 stairs per second, so after x seconds, he will have climbed 3x stairs. Therefore, the stairs he has left to climb is the total stairs minus the stairs he has climbed, which gives us the function:
f(x) = 24 - 3x
The domain of this function is the set of all x such that x is greater than or equal to 0 and less than or equal to 8, since Johan will finish climbing the stairs in 8 seconds. The range is the set of all possible stairs left to climb, from 24 down to 0, as Johan makes his way up.
To find f(5), we simply substitute 5 into the function:
f(5) = 24 - 3(5) = 24 - 15 = 9
So after 5 seconds, Johan has 9 stairs left to climb.
To find the value of x when f(x) = 18, we set up the equation and solve for x:
18 = 24 - 3x
3x = 24 - 18
x = 6/3
x = 2
Johan will have 18 stairs left after 2 seconds.