Relations and Functions
Characteristics of Linear Functions
Parallel/Perpendicular Lines
Alternate Forms of Linear Functions
Applications of Linear Functions
100
For a relation to be a function, each input must have ______ _____ output.
only one
100
What is the domain and range of a linear function?
all real numbers
RR
(-oo,oo)
100
Parallel lines have _______ slope
the same
100
What are the names of the three forms of a linear function?
Slope-Intercept
Point-Slope
Standard
100
What form of the linear function would we use to describe the given situation?
"In order to join a yoga club there is a $100 initial fee and a $5 fee for each class you attend."
slope-intercept form
200
Fill in the blanks:
Domain=_______=x-values
______=Outputs=_______
Inputs
Range, Y-values
200
________ is the point where the line touches the x-axis.
________ is the point where the line touches the y-axis.
x-intercept, y-intercept
200
Perpendicular lines have _______ _________ slopes
opposite reciprocal
200
What is the slope and the y-intercept of the following linear function?
y=-1/2x-7
m=-1/2
(0,-7)
200
What form of the linear function would we use to describe the given situation?
"You figured out that you could make $50 per pool to clean pools during the summer. You did, however, need to purchase some equipment to get started. After cleaning 3 pools you still were down a total of 15 dollars."
Point-Slope Form
300
Which of the following IS a function?
Table C
300
Find the rate of change of the given line:
m=-2
300
What would be the slope of a line PARALLEL to the given line?
y=-4x-8
-4
300
Put the following information into point-slope form:
slope=5
point=(-4,3)
y-3=5(x+4)
300
What form of the linear function would we use to describe the given situation?
"At a school play, children’s tickets cost $3 each and adult tickets cost $7 each. The total amount of money earned from ticket sales equals $210. Write a linear model that relates the number of children’s tickets sold to the number of adult tickets sold."
Standard Form
400
How do we know if the graph of a relation is a function or not?
Passes the vertical line test = function
400
Complete the mathematical phrases describing the end behavior of the given line:
as x->oo, f(x)->?
as x->-oo, f(x)->?
-oo
oo
400
What would be the slope of the line PERPENDICULAR to the given line?
y=-3/5x+6
5/3
400
Find the y-intercept given the following linear function in standard form:
3x+5y=15
(0,3)
400
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. Calculate the cost for using the taxi for 18 miles.
$16.50
500
Select 4 ordered pairs that will have a range of : {-2, 0}
(-3,-2) (0,-2) (1,-2) (3,0)
500
Is the following line increasing, decreasing, or constant(flat)?
What is the interval of increasing/decreasing/constant?
increasing
-oo<x<oo
RR
all real numbers
500
Are the following lines parallel, perpendicular, or neither?
y=4/3x-8
y-5=3/4(x-8)
neither, slopes aren't identical nor are they opposite reciprocals
500
Solve the following equation for y to turn into the slope-intercept form.
2x+5y=20
y=-2/5x+4
500
Ben walks at a rate of 3 miles per hour. He runs at a rate of 6 miles per hour. In one week, the combined distance that he walks and runs is 210 miles. Ben walks for 25 hours. For how many hours does he run?
22.5 hours