Function Vocab
Function Notation
Evaluate Functions
Story Graphs
Linear Functions
100
What is a relation?
A) A set of numbers
B) A set of ordered pairs
C) A type of shape
D) A type of animal
B) A set of ordered pairs
100
Given the function f(y) = y, what does f(y) represent?A) The input
B) The output
C) A type of animal
D) A type of shape
B) The output
100
Evaluate f(x) = -5x at x = -1.
f(-1) = 5
100
The graph below shows the percentage of U.S. population using the internet from 1996 to 2016.
a) The percentage of the U.S. population using the Internet is increasing overall.
b) The percentage of the U.S. population using the Internet increased the most from 2012 to 2016.
c) The percentage of the U.S. population using the internet is about the same between 2008 and 2012.
d) Over 70% of Americans were using the Internet in 2014.
a) The percentage of the U.S. population using the Internet is increasing overall.
c) The percentage of the U.S. population using the internet is about the same between 2008 and 2012.
d) Over 70% of Americans were using the Internet in 2014.
100
Given the function f(x) = -120x + 380. Identify the input, output, rate of change, and initial value.
Input: x
Output: f(x)
Rate of change: -120
Initial Value: 380
200
What is a function?
A) A type of relation where each input has only one output
B) Any set of numbers
C) A type of food
D) A type of color
A) A type of relation where each input has only one output
200
Given the function f(x) = 5x - 4, what does x represent?
A) The input
B) The output
C) A type of animal
D) A type of shape
A) The input
200
Evaluate f(x) = -x2 - 2x +7 at x = 2
f(2) = -22 - 2(2) + 7
f(2) = 7
200
A bug travels up a tree, from the ground, over a 30-second interval. It travels fast at first, then stops for 10 seconds, then proceeds slowly, speeding up as it goes. Which sketch best illustrates the distance (d) from the ground over the 30-second interval (t)?
B
200
A car can be rented for a flat fee plus an additional amount per day. The function f(x) = 55 + 50x models the total cost of the car in dollars after x days.
What does the 55 represent?
The flat fee for the rental.
300
What is a linear function?
A function in the form f(x) = a + bx whose graph is a straight line. Where a is the initial value (y-intercept) and b is the rate of change (slope).
300
Is this graph a function?
No, is does not pass the vertical line test.
300
Evaluate f(x) = 4 - 5x at x = m.
f(m) = 4 - 5m
300
The graph shows the number of quarts of water in a bathtub over time.
a) At one point, the person in the tub accidentally pushes the plunger away from the drain of the tub, removing some of the water. Which interval represents this?
b) Which interval shows the greatest change in the amount of water in the tub?
c) Which interval shows that the amount of the water in the tub is not changing for a period of 10 minutes?
a) The interval from 10 to 20 minutes
b) The interval from 25 to 45 minutes
c) The interval from 25 to 35 minutes
300
Kevyn has $50 saved in his piggy bank right now and each week he wants to save an additional amount of money. The total amount in his piggy bank can be modeled by the equation y = 10x + 50 where x is the number of weeks.
a) How much is Kevin adding to his piggy bank weekly?
B) Is this a linear function? Why or why not?
a) $10 dollars a week
b) Yes, because the rate of change is consistent, there is only one output for any input.
400
What is rate of change?
In a linear function, the constant rate of change is how much the f(x)- value changes when the input changes by 1.
It is represented by the value b in a linear function, f(x) = a + bx. On a graph, it is represented by the slope.
400
Is the set a function? {(2, 3), (0, 0), (5, 3), (8, -1)}
Yes, there is only one output for every input.
400
Evaluate g(x) = 5 - 2x for x = 4n + 2
g(4n + 2) = 5 - 2(4n + 2)
g(4n + 2) = -8n + 1
400
Janie decided to go on a bike ride. Sketch a graph based on the following situation:
- She left her house at 1:00 and rode at a constant rate for 10 minutes.
- Then, she got a flat tire, and worked to fix it for 5 minutes.
- Finally, she continued her ride at a rate of half the speed she started at.
Answers will vary.
400
A shop sells different flavors of popcorn by the pound. They charge $7 per pound plus an additional $3 for the tin to hold the popcorn.
Write a function that models this scenario.
f(x) = 7x + 3
500
What is initial value?
The starting value of a function. The output value when the input value is 0, or f(0). It is represented by the value a in a linear function, f(x) = a + bx. On a graph it is represented by the y-intercept.
500
Given the function f(x) = 3x - 5, what are the inputs for the given outputs.
Outputs: -11, -5, 10
f(2) = -11
f(0) = -5
f(5) = 10
500
The formula for compound interest can be modeled by: A = P(1 + (r/100))t, where A is the total money, P is the initial money deposited, r is the rate, and t is the time in years.
Given an initial deposit of $2500, how much would be in the savings account after 5 years at an interest rate of 4%?
$3041.63
500
Create a story to explain what happened to the water in the pool, as shown on the graph below.
Answers will vary.
500
Dina measured the diameter and circumference of multiple circular objects in her room. After analyzing her results, she determines that C = πd.
a) Is this a linear equation? Explain.
b) Is it a function? Explain.
c) If you were to graph C = πd, what does π
represent?
a) Yes, it has a ready rate of change, in this case π.
b) Yes, for each input there is only one output.
c) The slope or rate of change.