Relations & Functions
Given the Ordered pairs, identify the domain and range and determine if it is a function.
(-2,4),(-4,3),(-1,3),(-2,5)
Domain: -4, -2, -2, -1
Range: 3, 3, 4, 5
Function: No
Example of fraction if your slope is zero
Example of fraction if your slope is undefined
Zero: 0/8
Undefined: 7/0
Linear: straight line
Non-Linear: Curved line
Graph y=7/5x-6
Graph
What is the equation we use to find the direct variation? And what is the y-intercept always going to be?
m=y/x
Y-intercept is always 0
x: 0, 3, 7, 8, 12
y: -2, -2, -2, -2, -2
Domain: 0, 3, 7, 8, 12
Range: -2
Function: Yes
What are the four types of slope?
Positive, Negative, Zero, and Undefined
Is the equation Linear or Non-Linear? Solve.
2x-3y=15
Linear
y=2/3x-5
Graph y=-5
Correct Graph
When looking at a graph, what do we look for to see if it is a direct variation?
Make sure it goes through the origin
X= Domain
Y= Range
If you are just looking at your line on the graph given, how would you know if it is a positive or negative slope?
Positive: Up and to the right
Negative: Down to the right
In an equation, what are the three things we are looking for to make sure it is a linear function?
It is in slope-intercept form
x is not in the denominator
No exponents
Write the equation of line shown on graph in slope-intercept form
b=5
m=-6/4= -3/2
y=-3/2x+5
5x+2y=0
Yes, m=-5/2, y=-5/2x
If you are looking at a graph, what visual way can you use to figure out if the line is a function or not?
Vertical Line Test
Given the points (7, -5) and (1, -13), find the slope of that line, SIMPLIFY.
-13-(-5)/1-7
-8/-6=
4/3
Given the table, is the function Linear or Nonlinear?
x: 3, 8, 13, 18
y: -5, -1, 3, 7
Linear
It has the same rate of change on both sides
Graph 4x-3y=-21
y=4/3x+7
The distance traveled by a bus is directly proportional to the length of time it travels. If t took the bus 3 hours to drive 156 miles, identify the constant of variation and write an equation to represent the relationship.
y=distance; x=time
156/3= 52 mi/hr
y=52x