3.2 Graphing Functions and Relations

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Presentation transcript:

3.2 Graphing Functions and Relations

A relation is a function if and only if no 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.

Graph the relation and then state whether or not the relation is a function. 2.

Graph the relation defined by each of the following rules over the domain 3.

Graph the relation defined by each of the following rules over the domain 4.

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

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. slope steepness up down rise run vertical horizontal

Slope-Intercept Form The b represents the of the line. In other words, it’s where the line crosses the . y-intercept y-axis

Determine the slope and y-intercept of the lines below. 1. 2.

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.

Graph the equation. 4.

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 y x

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 x y

Find the x-intercept and y-intercept for the following equations. 5. 6.

Graph using intercepts. 7.

Graph using intercepts. 8.

9. Determine the value of k so that the given point will be on the graph of the given equation.

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.

Graph the Equation 11.

Absolute Value Graphs Absolute value graphs are in the shape of a . V

Use a table of values to graph the function. 12.

On your graphing calculator graph the following functions: What happened to the graph?

On your graphing calculator graph the following functions: What happened to the graph?

On your graphing calculator graph the following functions: What happened to the graph?

13. Without your calculator, graph the following functions. a.

13. Without your calculator, graph the following functions. b.