3.2 graphing functions and relations. another way that we can determine if a relation is a function...
TRANSCRIPT
3.2 Graphing Functions and Relations
• Another way that we can determine if a relation is a function is by looking at a graph of the relation.
• A relation is a function if and only if no
line intersects the graph more than once.
vertical
Graph the relation and then state whether or not the relation is a function.
1. 0,4 , 3,0 , 1, 2 , 3,1 , 4,0
Graph the relation and then state whether or not the relation is a function.
2. 1, 1 , 1,2 , 4,2 , 5, 3 , 2, 3
Graph the relation defined by each of the following rules over the domain
3.
2, 1,0,1,2, 3 y 5 x
Graph the relation defined by each of the following rules over the domain
4.
2, 1,0,1,2, 3 x y 3
3.3 Graphing Linear Equations
Linear Equations• Linear equations contain both an and a
• The graph of a linear equation is a .
• There are two forms of linear equations that we will look at:1. , which is in the form
2. , which is in the form
x y
line
Slope-intercept
Standard
y mx b
Ax By C
Slope-Intercept Form
• The m represents the of the line. The slope is the of the line. – When the slope is positive, the graph goes from left
to right.– When the slope is negative, the graph goes from
left to right.
– When graphing, the slope can be thought of as over , where the numerator determines the
displacement and the denominator determines the displacement between points on the line.
y mx bslope
steepnessup
down
riserun
verticalhorizontal
Slope-Intercept Form
• The b represents the of the line. In other words, it’s where the line crosses the
.
y mx b
y-intercept
y-axis
Determine the slope and y-intercept of the lines below.
1.
2.
y 1
2x 4
3y x 12
Graphing in Slope-Intercept Form
• First, make sure that the equation is in the form .
• Plot the first. Use this as your starting point.
• Use the slope to plot another point, using the idea of rise over run.
• Draw a line through your points with arrows on each end.
y=mx+b
y-intercept
Graph the equation.
3. y 2
3x 4
Graph the equation.
4. y 4x 7
Graphing in Standard Form
• One way to graph from standard form is to transform the equation into slope-intercept form.
• A second way to graph in standard form is to find the x-intercept and y-intercept. Plot the two points and draw a line through them.
x-intercept
• The x-intercept is in the form . So to find the x-intercept, you will need to substitute into the equation for and solve for .
, x 0
0 yx
y-intercept
• The y-intercept is in the form . So to find the x-intercept, you will need to substitute into the equation for and solve for .
• You can use this method to find the x and y-intercepts in slope-intercept form as well!
, 0 y
0 xy
Find the x-intercept and y-intercept for the following equations.
5.
6.
3x 2y 12
x
5y
61
Graph using intercepts.
7. 5x 2y 10
Graph using intercepts.
8. 6x 3y 12
9.Determine the value of k so that the given point will be on the graph of the given equation.
4x 6k 3y; 3, 10
Vertical and Horizontal Lines
• The equation for a vertical line is in the form: . The slope of a vertical line is
.
• The equation for a horizontal line is in the form: . The slope of a horizontal line is
.
x = #undefined
y = #
zero
Graph the Equation
10. y 5
Graph the Equation
11. x 3
Absolute Value Graphs
• Absolute value graphs are in the shape of a .V
Use a table of values to graph the function.
12. y x
• On your graphing calculator graph the following functions:
• Y1:
• Y2:
• Y3:
• What happened to the graph?
y xy x 3
y x 4
• On your graphing calculator graph the following functions:
• Y1:
• Y2:
• Y3:
• What happened to the graph?
y x2
y x 3 2
y x 2 2
• On your graphing calculator graph the following functions:
• Y1:
• Y2:
• Y3:
• What happened to the graph?
y x
y x 5 3y x 1 4
13. Without your calculator, graph the following functions.
a. y x 1 2
13. Without your calculator, graph the following functions.
b. y x 2 3