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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.
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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.
Linear Equations x y line Slope-intercept Standard 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
Slope-Intercept Form slope steepness up down rise run vertical horizontal • 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-Intercept Form y-intercept y-axis • The b represents the of the line. In other words, it’s where the line crosses the .
Determine the slope and y-intercept of the lines below. 1. 2.
Graphing in Slope-Intercept Form y=mx+b y-intercept 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.
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 x 0 0 y x 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 .
y-intercept 0 y 0 x y 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!
Find the x-intercept and y-intercept for the following equations. 5. 6.
9. Determine the value of k so that the given point will be on the graph of the given equation.
Vertical and Horizontal Lines x = # undefined y = # zero 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 .
Absolute Value Graphs V Absolute value graphs are in the shape of a .
On your graphing calculator graph the following functions: Y1: Y2: Y3: What happened to the graph?
On your graphing calculator graph the following functions: Y1: Y2: Y3: What happened to the graph?
On your graphing calculator graph the following functions: Y1: Y2: Y3: What happened to the graph?
13. Without your calculator, graph the following functions. a.
13. Without your calculator, graph the following functions. b.