Make a table of values for the following equation. Then graph the equation. y=|x|-2
Here is a table of values for the equation y = |x| - 2:
x | y
-----
-3 | 1
-2 | 0
-1 | -1
0 | -2
1 | -1
2 | 0
3 | 1
To graph the equation, plot the points in the table on a coordinate plane and connect them with a line. The graph will be a "V" shape, with the vertex at the point (0, -2) and the arms of the "V" extending upward. The graph should look like this:
(0, -2)
|
|
|
- - -
|
|
|
(3, 1) (1, -1) (-1, -1) (-2, 0) (-3, 1)
To make a table of values for the equation y = |x| - 2, we will substitute different values of x into the equation and calculate the corresponding values of y.
Let's choose some values for x and find the corresponding values of y:
For x = -3:
y = |-3| - 2
y = 3 - 2
y = 1
For x = -2:
y = |-2| - 2
y = 2 - 2
y = 0
For x = -1:
y = |-1| - 2
y = 1 - 2
y = -1
For x = 0:
y = |0| - 2
y = 0 - 2
y = -2
For x = 1:
y = |1| - 2
y = 1 - 2
y = -1
For x = 2:
y = |2| - 2
y = 2 - 2
y = 0
For x = 3:
y = |3| - 2
y = 3 - 2
y = 1
Now that we have a set of x and y values, we can plot these values on a graph.
On the x-axis, we will mark the values -3, -2, -1, 0, 1, 2, and 3.
On the y-axis, we will mark the values -2, -1, 0, 1.
Now, for each x-value, we will locate the corresponding y-value on the y-axis and plot a point:
(-3, 1)
(-2, 0)
(-1, -1)
(0, -2)
(1, -1)
(2, 0)
(3, 1)
Connecting these points with a smooth curve, we get the graph of the equation y = |x| - 2.
To make a table of values for the equation y = |x| - 2, we can choose different x-values and calculate the corresponding y-values. Here's a table with some x-values and their corresponding y-values:
| x | y=|x|-2 |
|---|---------|
| -3 | -5 |
| -2 | -4 |
| -1 | -3 |
| 0 | -2 |
| 1 | -1 |
| 2 | 0 |
| 3 | 1 |
Now let's plot these points on a graph to visualize the equation:
```
| *
| *
| *
| *
| *
| *
| *
| *
| *
| *
| *
| *
| *
| *
| *
| *
------------------------
-3 -2 -1 0 1 2 3
```
The graph of the equation y = |x| - 2 is a V-shaped graph that intersects the y-axis at y = -2.