All About Functions
In the function g(x) = r, which variable is the input and which variable is the output?
x is our input, and r is our output
Tyler filled up a pool, swam, then drained the pool. The function P, gives the depth of the water, in feet, t minutes after he began to drain the pool.
Explain the meaning of each statement:
P (0) = 5
At time 0 (when he started draining the pool), the height of the water was 5 feet.
In a function, we have the input and the output. We can call all possible inputs and outputs, domains and ranges. Which is input, which is output?
Domain - input
Range - output
A function z gives the height of a child in inches, when the child is t months old.
What does z (48) = 40 mean?
When the child is 48 months old, he/she is 40 inches tall
Tyler filled up a pool, swam, then drained the pool. The function P, gives the depth of the water, in feet, t minutes after he began to drain the pool.
Explain the meaning of each statement:
P (1) > P (4)
The pool is fuller at 1 minute than at 4 minutes
Function n represents the people in a store as a function of hours since it was open. The store is open from 8 am until 8 pm, and the peak number of customers was 112.
What is the domain of this function?
All real numbers between 0 and 12
A function n gives the weight of a giraffe in tons, when the giraffe is t years old.
What does n (20) = 2.1 mean?
When the giraffe is 20 years old, it weighs 2.1 tons.
Tyler filled up a pool, swam, then drained the pool. The function P, gives the depth of the water, in feet, t minutes after he began to drain the pool.
Explain the meaning of each statement:
P (8) = P (20)
The height of the water was the same at 8 minutes and 20 minutes
Function n represents the people in a store as a function of hours since it was open. The store is open from 8 am until 8 pm, and the peak number of customers was 112.
What is the range of this function?
All whole numbers from 0 to 112
We are given the statement :
Height is a function of time
Is time the input or the output?
Input
Tyler filled up a pool, swam, then drained the pool. The function P, gives the depth of the water, in feet, t minutes after he began to drain the pool.
Explain the meaning of each statement:
P (7) = 0
The pool was completely empty at 7 minutes
What is t when d (t) = 120?
t = 90 seconds
A ball is dropped from 10 feet in the air. it bounces until it comes to rest at time t= 20 seconds. The function m gives us the height of the ball as a function of time.
What is the domain of this function?
All real numbers from 0 to 20
A function l gives the population of a city in millions, for a certain year, y
What does l (2006) mean?
The population of the city in the year 2006.
Tyler filled up a pool, swam, then drained the pool. The function P, gives the depth of the water, in feet, t minutes after he began to drain the pool.
Explain the meaning of each statement:
P (3) - P (20) = 3
The difference in height between 3 minutes of draining and 20 minutes of draining is 3 feet
In words, what does d (0) represent in this situation?
The distance he is from home at time 0, or when he starts his walk
A ball is dropped from 10 feet in the air. it bounces until it comes to rest at time t= 20 seconds. The function m gives us the height of the ball as a function of time.
What is the range of this function?
All real numbers from 0 to 10.