Identifying functions

Identifying functions

Bring on more grid papers! In this chapter, we're going to study functions. Functions are notations that tell us what the value of y is for every value of x. By carrying out the vertical line test, we are able to find out the relationships of ordered pairs.
Basic Concepts: Solving linear equations by graphing, Relationship between two variables, Understand relations between x- and y-intercepts, Domain and range of a function
Related Concepts: Introduction to quadratic functions, Basic radical functions

Lessons

Relations: Sets of ordered pairs ( x , y )

Function: For every value of x, there is a value of y. It will need to pass the vertical line test.

One-To-One Function: For every one value of x, there is only one value of y, and vice versa. It will need to pass both vertical and horizontal line test.

Vertical line Test: A vertical line that intersects the graph of the equation only once when moves from across on the x-axis.

  • Introduction
    a)
    Equations VS. Functions

  • 1.
    Are the following sets of ordered pairs functions?
    a)
    (4,3), (2,6), (-3,4), (-2,5)

    b)
    (4,5), (4,-3), (2,6), (3,2)

    c)
    (3,6), (2,6), (5,3), (1,2)

  • 2.
    Which of the following is a function?

    Identifying functions
  • 3.
    Using the table of values to answer the questions below:
    a)
    X value -5 -3 -1 1 3
    Y value 3 1 -1 -2 -3
    Express the relations using ordered pairs, mapping notations and determine is it a function

    b)
    X value -5 -3 -1 1 3
    Y value 2 2 -1 -2 -3
    Express the relations using ordered pairs, mapping notations and determine is it a function

    c)
    X value -5 -5 -1 1 3
    Y value 2 3 2 3 -3
    Express the relations using ordered pairs, mapping notations and determine is it a function

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8.
Linear Functions
8.1
Relationship between two variables
8.2
Understand relations between x- and y-intercepts
8.3
Domain and range of a function
8.4
Identifying functions
8.5
Function notation
8.6
Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
8.7
Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)
8.8
Slope equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
8.9
Slope intercept form: y = mx + b
8.10
General form: Ax + By + C = 0
8.11
Point-slope form: y−y1=m(x−x1)y - y_1 = m (x - x_1)
8.12
Rate of change
8.13
Graphing linear functions using table of values
8.14
Graphing linear functions using x- and y-intercepts
8.15
Graphing from slope-intercept form y=mx+b
8.16
Graphing linear functions using a single point and slope
8.17
Word problems of graphing linear functions
8.18
Parallel and perpendicular lines in linear functions
8.19
Applications of linear relations
Basic Algebra
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