Is it a FUNCTION?
Interpret this function
Evaluate
Evaluate Graphs
Evaluate + Interpret
100
Determine if the given relationship is a function. Explain your answer.
This is a function because a function means that every input has exactly one output.
100
A --> 2
B --> 4
C --> 3
D --> 1
100
h(t) = -3t + 5
Find h(6)
h(6) = -3(6) + 5
h(6) = -18 + 5
h(6) = -13
200
Determine if the given relationship is a function. Explain your answer.
This is not a function because the input 1 has two outputs.
200
The function gives the number of people, in millions, who own a smartphone, years after year 2000. What does each equation tell us about smartphone ownership?
a. P(17) = 2,320
b. P(-10) = 0
a. In the year 2017, there were 2,320 million people who own a smart phone.
b. In the year 1990, there were 0 million people who own a smart phone.
200
f(x) = 6x - 4
Find f(3)
f(3) = 6(3) - 4
f(3) = 18 - 4
f(3) = 14
200
Evaluate for g(40).
g(40) = 3
300
Determine if the given relationship is a function. Explain your answer.
This is a function because the graph passes the vertical line test.
300
Use function notation to represent each statement.
In 2015, about 1.86 billion people owned a smartphone.
f(5) = 1.86
300
g(s) = 5(s - 3) + 17
Evaluate for g(4).
g(4) = 5(4 - 3) + 17
g(4) = 5(1) + 17
g(4) = 5 + 17
g(4) = 22
300
What is d(6) in the context of this problem?
d(6) = 3
The depth of water is 3 inches after 6 min.
300
The Flu is spreading through Columbia. The function below determines how many people have swine where t = time in days and S = the number of people in thousands. S(t) = 9t - 4. Find S(4).
S(4) = 32
400
Determine if the given relationship is a function. Explain your answer.
(-2, 1)
(-2, 3)
(0, -3)
(1, 4)
(3, 1)
This is not a function because the input -2 has two outputs.
400
The rule f(x)=50(0.85)x represents the amount of a drug in milligrams, 𝑓(𝑥), which remains in the bloodstream after 𝑥 hours. Evaluate and interpret each of the following:
𝑓(0)
𝑓(𝑥) < 6
f(x) = drugs in mg
x = hours in bloodstream
1. f(0) = 50(0.85)0
f(0) = 50(1) = 50
There are 50 mg of the drug after 0 hours.
2. The amount of mg is less than 6mg.
400
r(k) = 2k2 - 5k + 1
What is r(1)?
r(1) = 2(1)2 - 5(1) + 1
r(1) = 2(1) - 5(1) + 1
r(1) = 2 - 5 + 1
r(1) = -2
400
In the context of the problem, what is P(20) and explain its meaning.
P(20) = 5
After 20 seconds, the distance from the post is 5 feet.
400
If h(t)= -16t2+5t+7 models the path of an object projected into the air where 𝑡 is time in seconds and ℎ(𝑡) is the vertical height in feet. Find ℎ(5) and explain the meaning of the solution.
h(5) = -368
h(t) = height
t = time in seconds
After 5 seconds, the ball is -368 feet in the air.
500
Provide a definition for a function, input, and output.
500
You placed a cake in the oven and, after 45 minutes, you took it out. Let 𝑓 be the function that assigns to each minute after you placed the cake in the oven, its temperature in degrees Fahrenheit. Write a sentence for each of the following to explain what it means in everyday language.
𝑓(0) = 65
𝑓(5) < 𝑓(10)
𝑓(40) = 𝑓(45)
𝑓(45) > 𝑓(60)
f(t) = temperature
t = time in oven
- The temperature of the cake is 65 degrees after 0 min.
- The temperature of the cake at 5 min is less than the temperature of the cake at 10 min
The temperature at 40 min is the same as 45 min.
The temperature at 45 min is higher than at 60 min.
500
f(x) = x4 + 3x2 + 2x
Find f(2).
f(2) = (2)4 + 3(2)2 + 2(2)
f(2) = 16 + 3(4) + 2(2)
f(2) = 16 + 12 + 4
f(2) = 32
500
Here is a graph that represents function , which gives the height of a drone, in meters, seconds after it leaves the ground.
Describe which function value is greater:
a. f(0) or f(4)
b. f(2) or f(6)
a. f(4)
b. f(2)
500
The number of hours people in the United States spent playing video games each year from 1998 to 2001 can be modeled by the function f(x) = 11.9x + 46.4 where x is the number of years since 1998. Find the value of f(x) when x = 2. Explain what the solution means in this situation.
f(2) = 23.8 + 46.4
f(2) = 70.2
In 2000, people spent 70.2 hours each year playing video games.