how to model each rule with a table of values and a graph
What rules?
How do I make a table for f(x) equals x-3
To model each rule with a table of values and a graph, follow these steps:
1. Identify the rule: Determine the relationship between the variables you are working with. For example, if you have a rule that states "y is equal to 2x + 3", the rule is a linear equation where y depends on x.
2. Create a table of values: Choose different values for x and calculate the corresponding values of y based on the rule. Select values that will help you understand the pattern and behavior of the rule. For example, if you choose x = 0, 1, and 2, the corresponding values of y would be 3, 5, and 7, respectively. Include as many values as you need to clearly see the pattern.
3. Organize the data in a table: Create a table with two columns, one for x and one for y. List the chosen values of x in the x-column and the corresponding values of y in the y-column.
4. Plot the points on a graph: Take the values from the table and plot them as points on a coordinate plane. The x-values will be on the x-axis, and the y-values will be on the y-axis. For example, plot the points (0, 3), (1, 5), and (2, 7) on the graph.
5. Connect the points: Draw a line or curve through the plotted points. The line or curve represents the relationship between the variables according to the rule. In the case of a linear equation, the graph will be a straight line. Make sure the line or curve passes through as many points as possible.
6. Analyze the graph and table: Examine the graph and table together to understand the pattern and behavior of the rule. Look for trends, such as whether the relationship is linear, quadratic, exponential, etc. Notice the slope of the line and how it relates to the rule. Analyzing the graph and table will help you understand the rule visually.
Remember, these steps can be adjusted based on the specific rule you are working with. Different types of functions or rules may require different approaches to modeling with tables and graphs.