Identifying Functions
Function Characteristics
Linear Functions
Linear Equations & Inequalities
Non-Linear Functions
100
Which of the following relations is a function? Identify all that apply.
(a) {(0, 0), (0, 1), (0, 2)}
(b) {(0, 0), (1, 1), (2, 4)}
(c) {(0, 0), (1, 2), (1, 3)}
(b) and (c)
100
What is the domain of the function graphed?
all real numbers
100
The line segment on the graph below shows the altitude of a landing plane from the time its wheels are lowered to the time its wheels touch the ground. What is the slope of the line segment? Please answer in fraction form.
-25/3
100
Which ordered pair is NOT a solution to the linear inequality −3x+2y>−6? SHOW YOUR WORK.
(a) (0, −2)
(b) (0, 2)
(c) (2, 0)
(d) (0, 0)
(c) (2, 0)
100
Which of the following tables represents a quadratic function? How do you know?
D
200
A video club costs $25 to join. Each video that is rented costs $2.50. Let v represent the number of videos and let C represent the cost to rent the videos. Write an equation to represent this situation.
C=2.5v+25
200
The relationship between the weight of an object on the moon and on earth is given by the function y=6x, where x is the weight of the object on the moon and y is the weight of the object on earth. What is the most reasonable domain of this function?
all positive real numbers
200
The equation of a line is given by 6x+3y=6. What is the slope and y-intercept of this equation?
Slope = −2
Y-Int = 2
200
Write an inequality that best corresponds to the graph
200
Which type of function is graphed? How do you know?
Exponential - growing fast
Quadratic - curved like a U (other half is hidden)
300
The temperature of air in a room is 55oF. The thermostat is adjusted so that the temperature increases by 8oF per hour. Write a function that describes the temperature of the air over time. Create a table of values to show the temperature change over the first several hours.
y=8x+55
300
The scatterplot shows the relationship between the volume of water sealed in a boiler and the temperature of the steam generated. Select the statements that are true about this data.
(a) As the volume of water decreases, the temperature inside the boiler increases.
(b) Temperature and volume have a positive correlation.
(c) Temperature and volume have a negative correlation.
(d) As the volume of water increases, the temperature inside the boiler decreases.
(a), (c), and (d)
300
Write an equation for a linear function that passes through the points (2, −1) and (−1, −4). Hint: to write an equation of a line, you need the slope first then the y-intercept.
y=x−3
300
You pull out the plug from the bathtub. After 40 seconds, there are 13 gallons of water left in the tub. One minute after you pull the plug, there are 10 gallons left. Assume that the number of gallons varies linearly with the time since the plug was pulled.
Find the y-intercept (gallon-intercept). What does this number represent in the real world?
(0, 19)
This means there was originally 19 gallons of water in the tub.
300
Which of the following tables represents exponential data?
C
400
The line graph represents the price of a type of personal computer over a five-year period. Why is the graph misleading? What might someone believe because of the graph that could be untrue?
The intervals on the vertical axis are not equal. Someone might believe that the price decreased quickly from 2002 to 2004, then more slowly.
400
What is the value of the function f(x)=(x−5)2 when x=2?
9
400
Write an equation in slope-intercept form that models the relationship in the table below:
y=−2x+6
400
The velocity of an object fired directly upward is given by V=80−32t, where t is the time in seconds. When will the velocity be 16 feet per second?
when t=2 seconds
400
Listed below are several statements about the solutions of this equation:
x2+4x−12=0
Which of the following statements is NOT true?
(a) The solutions to the equation are x=−6 and x=2.
(b) The y-intercept is the solution to the equation.
(c) The graph of y=x2+4x−12 has two solutions.
(b) The y-intercept is the solution to the equation.
500
Graph −2x+4y=4
500
The table shown represents the function y=x+1. What is the y-intercept of this function?
(0, 1)
500
Mr. Mole left his burrow that lies below the ground and started digging his way deeper into the ground, digging at a rate of 1.8 meters per minute. His burrow is 4.5 meters below ground. How deep will Mr. Mole be underground after 5 minutes?
13.5 meters underground
500
Compare the graph and written function below. What is the greater maximum value of the two functions?
y=−4x2−4x+3
the equation has the greatest maximum of 4
500
State how you know the difference between a linear, exponential, or quadratic function.
Linear - adds or subtracts by the same amount each time
Exponential - multiply or divide by the same amount each time
Quadratic - increases then decreases or vice-versa