Graphing Linear Relations and Functions

Relations and Functions

Coordinate System

Domain is set of all first coordinates for ordered pairs (x)

Range is set of all second coordinates for ordered pairs (y)

Mapping - shows how each member at the domain is paired with each member of the range.

Function - special type of relation in which each element of the domain is paired with exactly one element of the range.

Vertical Line Test - determines if a relation is a function.
If you can touch the graph more than once when drawing a vertical line, it is NOT a function.

Linear Equation

Linear Equations contain 1 or 2 variables, with no variables having an exponent other than one.

Slope

 Parallel Lines - Non vertical lines with same slope
Perpendicular Lines  - Product of their slope is -1.

Ex: Find slope: (3,-2) and (-4,6)

Linear Equations

Point-slope  y-y₁ = m(x-x₁)
where m is slope and x₁ and y₁  is the coordinate

Ex: Give the slope intercept for the line that passes
through (-2,3) and (4,-1).
Find slope first:

Use that slope and either point
y- 3 = ⅔(x + 2)
y - 3 =   ⅔x + 1⅓
y = ⅔x + 4⅓

Statistics - Scatter Plots

Points graphed that do not form a line.

Best Fit Line - approximate linear relationship for a scatter plot.

Prediction Equation - use any two points and calculate an equation.

Special Functions

Constant Functions
Slope is 0 then y = -1
Undefined slope then x = 2

GRAPH INEQUALITIES

EX: Graph the inequality: 2y > 3x - 8
Solve for y:
y > 3/2x - 4

Scroll down for steps:

Piecewise Function:

SHIFTS OF GRAPHS
y = a|x| if a<1 get wider
y = a|x| if a>1 get narrower
y = |x+h| moves left h units
y = |x-h| moves right h units
y = |x|+k moves up k units
y = |x|-k moves down k units
y = -|x| means it reflects across the x-axis(graph is flipped)

 EX: Graph the function:y = -2|x+1|-3

moves left 1, down 3, narrower by 2 and reflects across the x-axis.

Example Problems

1.Give the domain and range for the following relation and tell whether it is a
     function:    {(3,-2), (5,1), (-4,3), (5,6), (0,8) .

2. Find the slope between (4,-5) and (-3,2).

3. Give slope and y-intercept for the line: -8x + 4y = 12

4. What is the standard form of the line that passes through (-4,8) and has
    slope of -3?

5. What is the slope-intercept form of the equation of the line that passes
    through (4,1) and (-2,3)

6. Write equation of the line that is parallel to y = 7x - 8 and passes through (2,6)

7. Write equation of the line that is perpendicular to y = 4x-5 and passes
    through (-1,2).

8. Find slope and y-intercept and use to graph the line 6x + 8y = 16