Graphs are used to represent data in all areas of life. Finding a function rule for real-world data allows you to make predictions about what may happen.Īnalyze the Graph of a Real-World Situation It is important we make sure this rule works for all the points on the curve. These variables are related to each other by a rule. The coordinate points give values of dependent and independent variables. From a graph, you can read pairs of coordinate points that are on the curve of the function. In many cases, you are given a graph and asked to determine the relationship between the independent and dependent variables.

The equation of the function is f(x)=1.5x. We can see that for every minute the distance increases by 1.5 feet. Make a table of values of several coordinate points to identify a pattern. Figure 4.1.5.6įind the function rule that shows how distance and time are related to each other for the graph above about inchworms: The graph below shows the distance that an inchworm covers over time. For now, we will look at some basic examples and find patterns that will help us figure out the relationship between the dependent and independent variables. There will be specific methods that you can use for each type of function that will help you find the function rule. In this course, you will learn to recognize different kinds of functions. Can Joseph ride 212 rides? Of course not! Therefore, we leave this situation as a scatter plot. By connecting the points we are indicating that all values between the ordered pairs are also solutions to this function. The dots are not connected because the domain of this function is all whole numbers. The green dots represent the combination of (r,J(r)). Using the table below, let's construct the graph of the function such that x is the number of rides and y is the total cost: r Suppose we wanted to visualize Joseph’s total cost of riding at the amusement park. The function that represents the cost of riding r rides is J(r)=2r. Figure 4.1.5.4Ĭonsider a student named Joseph, who is going to a theme park where each ride costs $2.00. The first quadrant is the upper right section, the second quadrant is the upper left, the third quadrant is the lower left and the fourth quadrant is the lower right.

When referring to a coordinate plane, also called a Cartesian plane, the four sections are called quadrants. Figure 4.1.5.3įor a positive x value we move to the right.įor a negative x value we move to the left. We show all the coordinate points on the same plot. Plot the following coordinate points on the Cartesian plane: To graph a coordinate point such as (4, 2), we start at the origin.īecause the first coordinate is positive four, we move 4 units to the right.įrom this location, since the second coordinate is positive two, we move 2 units up. The second coordinate represents the vertical distance from the origin. Data points are formatted as (x,y), where the first coordinate represents the horizontal distance from the origin (remember that the origin is the point where the axes intersect).

Once a table has been created for a function, the next step is to visualize the relationship by graphing the coordinates of each data point.

Graphing points on a coordinate plane