Relations and Functions (pre cal gr. 10)

Relation

associates the elements of one set with the element of another set.

Set

a collection of distinct objects.

Elements

inside set and are one object in a set.

How to write a set to list elements?

Put in curly brackets outsides and then in normal brackets for elements.

Domain

(x) is the set of the first elements in a relation. It is also called the input value and the independent variable.

Range

(y) is the set of the second elements in a relation. It is also called the output value and the dependent variable.

Function

A special type of relation where each element in the domain is associated with exactly 1 element in the range. One value of (x) gives 2 or more values in the range (y), then that not a function.

Function notation

A rule or relationship of a function. It tells us what the function does to input value x, which is to double it.

Straight lines are used in graphs when the change in variables is…

constant

Curves are used in graphs when the change in a variable in the independent and dependent variable…

is not constant.

Scatterplot

A type of graph that displays values for 2 variables for a set of data. A scatterplot can suggest a correlation or relationship between variables.

Discrete data

Data that can only take on certain values. (#of students in a class- u cannot have half a student) and discrete points are not connected “single points”

Continuous data

Data that can take any value within the range (e.g. temp) and points are connected

Vertical line test

If one edge of the ruler intersects the graph at no more than 1 point, the graph represents a function.

Solid dots mean…

point is included (square brackets)

Hollow dots mean…

point is not included (normal brackets)

Set notation

shows relationship in words

Interval notation

Uses numbers and square and round brackets

For a linear relation, a constant change in the independent variable results in a….

constant change in the dependent variable.

y=mx+b

explain what each variable means

y is the dependent variable

x is the independent variable

b is the initial amount

m is the rate of change

The rate of change can be expressed as:

m= change in dependent variable/ change in independent variable (or rise/run)