Features of Functions
More Features of Functions
Analyzing Functions
Interpreting Graphs
Mixed Review
100
On the interval [0,5]
What is the interval of increase?
100
What are the coordinates of an x-intercept?
(3,0) and (8,0)
100
Chris earns $15 per x hour working at a grocery store, modeled by the function f(x) = 15x.
f(5) =
f(5) = 15(5)
f(5) = 75
100
If x = 3, f(3) =
0
100
The inputs/x-values of a function
What is the domain?
200
On the interval [-4, 1]
What is the range?
200
The maximum of the function
(5,1)
200
A car travels at a constant speed of 60 miles per hour, represented by the function v(t) = 60t, where t represents time in hours.
What does v(3) = 180 mean in context
After 3 hours, the car has traveled 180 miles.
200
If f(x) = 1, then x =
5
200
When the x-values increase but the y-values decrease
What is the interval of decrease?
300
On the interval [-5, 8]
What is the domain?
300
The domain of the function
[0,21]
0<x<21
300
The distance that a dog can run in feet is measured based on how many seconds he has been running. This distance can be modeled by the function d(t) = 10t, where d(t) is the distance in feet at time t in seconds.
How far has the dog run in 3 seconds?
30 feet
3 seconds means t = 3
300
f(4) =
0.5 or 1/2
300
f(x) = g(x). 
(4,2)
400
On the interval [-3.5, 10]
What is the range?
400
The interval of decrease
[-5,0]U[5,8]
400
A tank is being filled with water at a constant rate of 3 liters per minute. This rate can be modeled by the function V(t) = 3t, where V(t) is the volume in liters at time t in minutes.
After 27 minutes, the tank has 81 liters. Write in function notation
V(27) = 81
400
If f(x) = 0, what are the two possible values of x?
3 and 8
400
The height of a ball after t seconds is given by the function h(t).
If you are asked to find h(3), are you finding the input or the output? What does it represent in this situation?
You are finding the output.
It represents the ball’s height after 3 seconds.
500
On the point (0, 10)?
Hint: 2 answers
What are the y-intercept and the maximum?
500
The minimum of the function
(0, -4)
500
A taxi ride costs $4 to start, plus $2 per mile. This can be modeled by the function c(x) = 2x + 4, where c(x) is the cost ($) after x miles.
Calculate the value of x if c(x) = 36 and explain what that means in this context.
x = 16 miles
The taxi costs $36 to drive 16 miles.
c(x) = 36
2x + 4 = 36
2x = 32
x = 16
500
Which is greater, f(5) or f(8)?
f(5) = 1
500
A candle burns at a steady rate of 2 inches per hour. The function h(t)=12−2t represents the candle’s height (in inches), where t is the time in hours since the candle was lit.
If h(t)=4, what is the value of t, and what does this mean in the context of the problem?
After 4 hours, the candle’s height will be 4 inches.