Relations and Functions
1. {(-4,2), (-1,5), (3,7), (6,-2)}
What is the domain of the function?
Domain: {-4, -1, 3, 6}
At week 2, Bella's grade was a 90. At week 10, her grade was an 82. Find the rate of change of her grade between the weeks.
m = -1 pt/wk
What is the slope of a horizontal line?
0
The U.S. Bureau of the Census predicted that the population of Florida would be about 17.4 million in 2010 and then would increase by about 0.22 million per year until 2015. Which of the following linear models predicts the population, y, of Florida (in millions) in terms of x, the number of years since 2010.
A. y = 17.4x + 0.22
B. y = -0.22x + 17.4
C. y = 0.22x + 17.4
D. y = -17.4x + 0.22
C
Is this equation linear or nonlinear? Convert to slope-intercept form if necessary.
y = 2x - 4
linear
Relation: {(1,3), (2,5), (3,7)}
What is the range?
Answer: {3, 5, 7}
A tank had 18 gallons of water. After 6 hours it had 6 gallons left. Find the rate of change.
-2 gal/hr
What is the slope of a vertical line?
Undefined
Cameron is designing a calendar as a fund-raising project for math class. The cost of printing is $500, plus $2.50 per calendar. Write an equation in slope-intercept form that models the total cost of printing the calendars.
y = 2.5x + 500
What is slope-intercept form?
What is standard form?
y = mx + b
ax + by = C
Relation: {(1,4), (2,6), (3,8), (4,10)}
Is this relation a function?
Yes
A climber is on a hike. After 2 hours he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet. What is the average rate of change?
75 ft/hr
Find slope between (2,4) and (4,8)
m = 2
Harry's phone plan costs $25 a month. However, each time he makes a call, the carrier charges him $0.25. Harry's mom wants to know how much the phone bill will be if he makes 20 calls this month. Write and evaluate an equation that would help Harry's mom to figure out the cost of the phone bill.
y = .25x + 25
when x = 20, total cost is $30
Is this equation linear or nonlinear? Convert to slope-intercept form if needed.
2x - 4y = 8
y = 1/2x - 4
linear
Relation: {(2,5), (2,7), (3,8)}
Is it a function?
No, x=2 has 2 outputs
A plane left Chicago at 8:00 A.M. At 1: P.M., the plane landed in Los Angeles, which is 1500 miles away. What was the average speed of the plane for the trip?
300 mph
Find the slope between the points (8,2) and (11,3)
m = 1/3
An airplane 30,000 feet above the ground begins descending at a rate of 2,000 feet per minute. Write an equation to model the situation. Find the altitude of the plane after 5 minutes.
equation: y = -2000x + 30,000
after 5 mins, the plane would be at 20,000 ft.
Is this equation linear or nonlinear?
y = -3/x
nonlinear
Given the function and its domain, find the range.
Domain = {0, 4, 6}
Function: y = 3x + 10
range = {10, 22, 28}
A rocket is 1 mile above the earth in 30 seconds and 5 miles above the earth in 2.5 minutes. What is the rocket's rate of change in miles per second? What about miles per minute?
1/30 miles per second
2 miles per minute
What is the slope formula?
m = y2 - y1 / x2 - x1
When visiting Baltimore, MD, you need to rent a taxi to get from your hotel to the National Aquarium. The taxi company charges a flat fee of $3.00 for using the taxi and $0.75 per mile. How many miles away is the aquarium from the hotel if you paid $30?
36 miles
Given the equation in standard form, convert it into slope-intercept form and determine if it is linear or nonlinear. Explain why it is either linear or nonlinear.
3x - 6y = 15
y = 1/2x - 5/2
linear, exponent of one, constant slope.