8th Grade Algebra (AP)
f(x)=-3x
Model the rule with a table of values and a graph.
x f(x)
-3 -3(-3)=9
-2 -3(-2)=6
-1 -3(-1)=3
...
5 -3(5) = 15
Complete the table and draw the graph.
To model the rule f(x) = -3x with a table of values, you need to choose a few values for x and then use the function to calculate the corresponding values for f(x). Let's choose a range of x values and calculate the corresponding f(x) values:
x | f(x)
--|-----
-3| 9
-2| 6
-1| 3
0| 0
1| -3
2| -6
3| -9
To find the values of f(x), we substitute the chosen values of x into the given function f(x) = -3x. For example, when x is -3, f(x) = -3(-3) = 9.
Now let's move on to graphing the function. On a coordinate plane, plot the points from the table of values: (-3, 9), (-2, 6), (-1, 3), (0, 0), (1, -3), (2, -6), (3, -9). Connect the points with a straight line.
|
| * (-3, 9)
| *
| *
| *
| *
| *
| *
------+------------------
|
-3
The graph of the function f(x) = -3x is a straight line that passes through the origin (0, 0) and has a negative slope of -3, because for every 1 unit increase in x, y (or f(x)) decreases by 3 units.
By using a table of values and graphing, we can model the rule f(x) = -3x.