Relations & Functions
What are two way you can know if a relation is a function?
Vertical Lin Test & Check the x-values
{(1,2),(2,3),(3,4),(4,5)}
yes each input has one output
2x+5=15
x=5
A way of representing how things change over time
A Function
A relation where each x-value has only one corresponding y-value
A Function
Which of these are a functions?
A:`{(0,1),(1,2)(2,3),(3,4)}`
B:`{(0,1),(1,1),(2,1),(3,1)}`
C:`{(0,1),(1,2),(0,3),(2,4)}`
Relation A is a function
A circle drawn on a coordinate plane
no, circles fail the vertical line test
2x/5+7=15
x=8
A function that makes a straight line when graphed
Linear
The highest y-value of a function/graph
Maximum
What is the Domain and Range?
`{(-2,4),(-1,1),(0,0),(1,1),(2,4)}`
Domain:`{-2,-1,0,1,2}`
Range:`{0,1,4}`
{(1,2),(1,3),(2,4),(3,5)}
no because input 1 is mapped to two different outputs
7x-3=18
x=3
A Function with an equation with a number raised to the power of X
Exponential
Where a function/graph crosses the x-axis
is f(x) = 2x + 1 a function if x equals 3?
It is a function
y=2x+3
yes
3(x-4)+2=14
x=8
Multiplying a number outside of parentheses by each term within those parentheses
Distributive Property
A way of determining if a scatterplot or graph is a function or not
Vertical Line Test
Which of the following sets of ordered pairs represents a function?
A =`{(1,2),(2,3),(2,9),(4,5)}`
B =`{(5,5),(6,5),(7,5),(8,5)}`
C =`{(7,1),(6,7),(8,5),(1,2)}`
C, is the function
a sideways parabola
no because one x-value has two possible y-values
7x+15+25-10+3x=100
x=7
Data the trends downward
Negative Correlation
A type of relation involving two ovals and arrows showing how each x-value maps to each y-value
Mapping