Vocabulary
A _____________________ of a function is a value of the function that is less than or equal to all the other values.
Minimum
Function f(x) gives the height of a bouncy ball after x seconds. What does the y intercept tell you about the bouncy ball?
The height the ball starts at
Given the function f(x)=2x+1, find f(4)
f(4) = 9
Refer to Graph A. At what value of t does f(t)=15? What feature of the graph is it?
0 Seconds, y intercept
What does a straight line tell you about rate of change?
constant rate of change
A ______________________ takes inputs from one set and assigns them to outputs from another set, assigning exactly one output to each input
Function
Function f(x) gives the height of a bouncy ball after x seconds. What does the x intercept tell you about the bouncy ball?
The time when the ball hits the ground.
The function f(y) = p gives the population (in millions), p, for y years after 2000. What does f(23)=1.5
The population in 2023 is 1.5 million
Refer to graph A. What is the range of the function?
0 to 35 meters
Refer to graph A. At what interval is the function increasing?
0 to 2 seconds
The _____________________ of a function is the set of all possible input values.
domain
Function f(x) gives the height of a bouncy ball after x seconds. Would the graph have only one relative maximum or minimum? Explain.
No, the graph would be wavelike because the ball would continue bouncing up and down.
If a function h models temperature in degrees Celsius after t hours as h(t)=−2t+20 interpret h(3) in context.
The temperature after 3 hours
Refer to Graph B. Evaluate f(6).
9 meters
Refer to Graph B. Find the rate of change from 2 seconds to 5 seconds.
10/3 meters per second = 3.3 repeated meters per second
A Function is _________________ if its outputs get smaller as the inputs get larger
decreasing
Function f(x) gives the height of a bouncy ball after x seconds. The ball is dropped from 6 feet above the ground and bounces for 8 seconds. What is the domain of the function?
0 to 8 seconds (continuous)
You earn $10 per hour plus a one-time $30 bonus. Write an explicit linear function f(h) giving total pay for h hours.
f(h) = 10h + 30
Refer to graph B. What is the domain of the function?
2 to 15 seconds
Refer to graph B. Find the rate of change from 5 seconds to 9 seconds.
-1/4 meters per second = -0.25 meters per second
The ________________________ of a function f between inputs a and b is the change in the outputs divided by the change in the inputs
Average Rate of Change
Function f(x) gives the height of a bouncy ball after x seconds. The ball is dropped from 6 feet above the ground and bounces for 8 seconds. What is the range of the function?
0 to 6 feet (continous)
function f shows that the number of people in the park is a function of time, in hours, since the park has opened. Write function notation to represent 80 people being in the park after 45 minutes of the park being open.
f(0.75) = 80
Refer to graph B. what values of t make f(t) = 0 true?
2 seconds, 14 seconds
Refer to Graph B. Find the rate of change from 9 seconds to 15 seconds.
- 11/6 meters per seconds = - 1.83 repeated meters per second