Unit 3 Relations and Functions

​Relations and Functions

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The plane containing the x and y axes​. It is formed by the intersection of two number lines, the horizontal axis and the vertical axis

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Coordinate Plane

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​The horizontal number line (axis) on a coordinate plane.

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x-axis

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the vertical number line (axis) on a coordinate plane.​

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y-axis

​the four regions into which the x and y axis separate the coordinate plane.

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quadrants

the point where the two axes intersect at their zero points. (0,0)

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origin

A set of numbers or coordinates used to locate any point on a coordinate plane, written in the form (x,y)​

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ordered pair

the first number in an ordered pair​

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x-coordinate

the second number in an ordered pair.​

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y coordinate

a function of points that are not connected

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discrete graph

​a function that can be graphed with a line or smooth curve

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Continuous Graph/Function

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​a set of ordered pairs

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Relation ​

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​the set of the first numbers of the ordered pairs in

a relation

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Domain

​the set of second numbers of the ordered pairs in a relation.

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Range

​illustrates how each element of the domain is paired with an element in the range

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Mapping

​a relation in which each element of the domain is paired with exactly one element of the range

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Function

​a way to name a function that is defined by an equation. In function notation, the equation y=3x-8 is written as

f(x)=3x-8

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Function Notation

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​a value substituted ofr an x-value in a function

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Input

​the result of substituting a value into a function

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Output

if any vertical line passes through no more than one point of the graph of a relation, then the relation is a function​

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Vertical Line Test

the x-intercepts of the graph of a function: the points for which f(x)=0​

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Zeros

​a numerical pattern that increase or decreases at a constant rate or value. The difference between successive terms of the sequence is constant

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Arithmetic Sequence

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the difference between the terms in an arithmetic sequence​

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Common Difference

the formula to find the nth term in a sequence.

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Arithmetic Sequence Formula​

Multiple Choice

What is a function?

• a relation in which each element of the domain is paired with exactly one element of the range

• ​the four regions into which the x and y axis separate the coordinate plane.

• ​a set of ordered pairs

• ​the result of substituting a value into a function

Multiple Choice

By looking at the images below. Identify the x-axis

Multiple Choice

By looking at the images below. Identify the y-axis

Multiple Choice

How many quadrants are on a coordinate plane?

• 1

• 2

• 4

• 6

Multiple Choice

Select the image below that identifies the origin.

Multiple Choice

Identify the domain of the following relation.

{(3,2) (-1,5) (7,3) (2,-3)}

• D: {-1,3,2,7}

• D: {-3,2,3,5}

Multiple Choice

Identify the range of the following relation.

{(3,2) (-1,5) (7,3) (2,-3)}

• R: {-1,3,2,7}

• R: {-3,2,3,5}