Given the function below, fill in the table of values and use the table values to graph.
[tex]y=-3 x[/tex]
| x | y=-3x |
|---|---|
| -3 |
| -2 |
| -1 |
| 0 |
| 1 |
| 2 |
| 3 |
Answer (2)
Calculate y for each x value using y = − 3 x .
For x = − 3 , − 2 , − 1 , 0 , 1 , 2 , 3 , the corresponding y values are 9 , 6 , 3 , 0 , − 3 , − 6 , − 9 .
Fill in the table with these values.
Plot the points and draw a line through them to graph the function. The table values are:
x
y
-3
9
-2
6
-1
3
0
0
1
-3
2
-6
3
-9
See graph for the plot of these points.
Explanation
Understanding the Problem We are given the function y = − 3 x and asked to complete the table of values for x = − 3 , − 2 , − 1 , 0 , 1 , 2 , 3 . Then, we will use these values to graph the function.
Calculating y values To fill in the table, we need to calculate the value of y for each given x value using the function y = − 3 x .
Calculating y for x = -3 For x = − 3 , we have y = − 3 ( − 3 ) = 9 .
Calculating y for x = -2 For x = − 2 , we have y = − 3 ( − 2 ) = 6 .
Calculating y for x = -1 For x = − 1 , we have y = − 3 ( − 1 ) = 3 .
Calculating y for x = 0 For x = 0 , we have y = − 3 ( 0 ) = 0 .
Calculating y for x = 1 For x = 1 , we have y = − 3 ( 1 ) = − 3 .
Calculating y for x = 2 For x = 2 , we have y = − 3 ( 2 ) = − 6 .
Calculating y for x = 3 For x = 3 , we have y = − 3 ( 3 ) = − 9 .
Completed Table and Graphing Now we have the following table:
x
y = -3x
-3
9
-2
6
-1
3
0
0
1
-3
2
-6
3
-9
We can plot these points on a coordinate plane and draw a line through them.
Examples
Understanding linear functions like y = − 3 x is crucial in many real-world scenarios. For instance, imagine you're tracking the descent of a submarine. If the submarine descends at a rate of 3 meters per second, the function y = − 3 x can represent its depth ( y ) after x seconds. This allows you to predict the submarine's depth at any given time, which is vital for navigation and safety. Similarly, this concept applies to calculating depreciation, temperature changes, or any consistent rate of change.
To complete the table for the function y = − 3 x , we calculated both the x and corresponding y values, resulting in seven points. Plotting these values on a graph demonstrates the linear relationship, which slopes downward as x increases. This helps visualize the function clearly.
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