Relations and Functions
Representations of Functions
Linear Functions
Comparing Linear and Nonlinear Functions
Analyzing and Sketching Graphs
100
Determine whether the relation is a function.
Find the domain and range.
What is ( -1,4), (7,6), (3,6), (5,0), (7,8)
The relation is not a function.
Domain: 1,3,5,7.
Range: 4,0,6,8
100
Determine whether the table represents a function.
Input: 2,4,6,8,10.
Output: 2,2,3,3,4.
Is the table a relation?
Find the domain and range.
What is Yes, this table is a relation?
Domain: 2,4,6,8,10
Range: 2,3,4
100
A _ is a function whose graph is a nonvertical line. A _ can be written in the form of y=mx + b, where m is the slope and b are the y-intercept.
What is Linear function?
100
The graph of linear function shows a constant rate of change. A _ does not have a constant rate of change.
So, its graph is not a line.
What is a Nonlinear Function?
100
The graph shows the location of a pelican relative to your location.
a. Describe the path of the pelican.
b. Write an explanation for the decrease in the vertical distance of the pelican.
a. It decreases Fastly then slow decreases again.
b. The pelican flying decreases Fastly then as the evening comes it decreases slowy.
200
The mapping diagram represents the lengths (in centimeters) of a rubber band when different amounts of force (in Newtons) are applied.
Determine whether the length of a rubber band a function of the force applied to the rubber band?
Find the domain and range.
Describe the relationship between the length of a rubber band and the force applied to the rubber band.
What is Yes?
Domain: 0, 0.07, 1.4, 2.1.
Range: 5, 7, 9, 11
0.7 x 7= y
200
Determine whether the graph represents a function.
Is this relation a function?
Find the domain and range.
What is The is relation is a function?
Domain: -4,0, 2
Range: -4, -3, -1, 1, 3
200
Use the table to write a linear function that relates.
X= -2, -1, 0, 1.
Y= 2, 2, 2, 2.
y=?
What is -2x + 2?
200
Does the equation represent a linear or nonlinear function?
y= 1- x2
Is it nonlinear or linear?
Explain.
What is Nonlinear?
It can't be written in slope intercept form.
200
A fully charged battery loses its charge at a constant rate until it has no charge left. You plug it in, and it fully recharges at a constant rate. Then it loses its charge at a constant rate until it has no charge left. Choose the sketch of a graph that represents this situation.
Which one is it?
What is
?
300
Determine whether the relation is a function. Then find the domain and range.
(-3, -9), (-2, -7), (0, -3), (-1, -1), (1,5)
Is the relation a function?
yes or no?
domain and range
Is the relation a function?
yes!
Domain: -3, -2, 0, -1, 1.
Range: -9, -7, -3, -1, 5.
300
Determine whether the graph represents a function.
Is this relation a function?
Find the domain and range.
What is This relation is not a function?
Domain: -1 < x and x < 3
Range: -2 < y and y < 3.
300
You and your friend are saving money to buy bicycles that cost $175 each. You have $45 to start and save an additional $5 each week. The graph shows the amount y (in dollars) that your friend has after x weeks. Who can buy a bicycle first?
_ can buy a bicycle first.
Justify your answer.
What is Your friend?
It takes 25 weeks for my friend and 26 weeks for me.
300
Does the graph represent a linear or nonlinear function?
Is it nonlinear or linear?
Explain.
What is Linear?
The graph is a line.
300
Two rowing teams are in a race. The graph shows their distances from the finish line over time. Describe the speed of each team throughout the race.
Determine which team wins first.
what is the speed decreases slowly than increases and gets there before Team B?
Team A finishes first.
400
Input: Output:
1,2, 3,4,5, _ -1, -9, -13, _, -21
Describe the relationship between the inputs and outputs in the diagram. Then complete the diagram.
Is there more than one possible answer?
yes, or no?
Explain your reasoning.
Input: Output:
1,2,3,4,5,6 -1, -9, -13, -17, -21
The input is counting by 1's and the output is counting by 4's.
No, because then the relations wouldn't be a function.
400
Determine whether the graph represents a function. Then find the domain and range.
Does the graph represent a function?
Find the Domain and range?
What is yes, the graph does represent a function?
Domain: -2 < x and x < 4
Range: 0 < y and y < 3
400
An unmanned aerial vehicle (UAV) is used for surveillance. The table shows the height y (in thousands of feet) of the UAV x minutes after it begins to descend from cruising altitude.
Minutes, x Height (thousands of feet), y
0, 10, 20. 65, 55, 45.
a. Write and graph a linear function that relates y to x.
y=?
b. Interpret the slope and the y-intercept.
What is -1x + 65?
a. (0,65) and (5,55) the is a diagonal line with those two points close by.
b. Every ten minutes you lose 10 elevations.
400
The loudness of sound is measured in decibels (dB). The graph shows the loudness y of a sound (in decibels) x meters from the source of the sound.
Is the relationship between loudness and distance linear or nonlinear?
Approximate the loudness of the sound 12 meters from the source.
What is Nonlinear?
The sound is 84 decibels.
400
The graphs show the movements of two airplanes over time. Describe the movement of each airplane.
What is at the beginning of both airplane B and A they take off at a consistent rate above the ground, then the height of the above the ground drops and Fasty stays at a consistent rate. Then the height of the above the ground increases Fastly?
500
MODELING REAL LIFE The normal pressure at sea level is 1 atmosphere of pressure (1 ATM). As you dive below sea level, the pressure changes. The mapping diagram represents the pressures at different depths.
a. Complete the mapping diagram.
b. Determine whether the pressure is a function of depth.
c. Describe the relationship between pressure and depth.
d. Select the ordered pairs represented in the mapping diagram. Then plot the ordered pairs in a coordinate plane.
What do you notice about the points?
= 4 am, 5am, 6am.
The relation is a function.
Domain: 0,10, 20, 30, 40, 50
Range: 1, 2, 3, 4, 5, 6
The pressure increases by 1 ATM for each 10-meter increase in the depth.
- (0, 1)
- (10, 2)
- (20, 3)
- (30, 4)
- (40, 5)
- (50, 6)
The go in a diagonal line.
500
Find the Value of y when x=5
y= 7 - 3x
What is when x= 5, y=-8?
500
The table shows the number of y of calories you burn after x hours of jogging.
a. Write and graph a linear function that relates Y to x.
b. Intercept the slope and y-intercept.
what is m= y2 - y1
x2 - x1 = 800 - 1600 and 2-4 = -800/-2 = 400
b. The slope indicates that you burn 400 calories per hour of jogging. The y-intercept indicates that you begin jogging, you have not burned any calories.
500
In their first year, Show A has 7 million viewers and Show B has 5 million viewers. Each year, Show A has 90% of the viewers it had in the previous year. Show B loses 200,000 viewers each year.
a. Determine whether the function relating the year to the number of viewers is linear or nonlinear for each show.
b. Which show has more viewers in its sixth year?
The function for Show A is linear.
The function for Show B is Nonlinear.
b. Show A has more viewers in its sixth year.
500
MODELING REAL LIFE The graph shows the natural gas usage for a house.
a. Describe the change in usage from January to March.
b. Describe the change in usage from March to May.
a. The usage decreases at an increasing rate
b. The usage decreases at a decreases rate.