Use integer values of x from –3 to 3 to graph the equation.
y = –|x|
a
b
c
d
Answer:
a) x: -3 -2 -1 0 1 2 3
y: 3 2 1 0 1 2 3
To graph the equation, y = –|x|, we need to plot points using integer values of x from -3 to 3.
First, let's calculate the values of y for each corresponding value of x:
When x = -3:
y = -|-3| = -3
When x = -2:
y = -|-2| = -2
When x = -1:
y = -|-1| = -1
When x = 0:
y = -|0| = 0
When x = 1:
y = -|1| = -1
When x = 2:
y = -|2| = -2
When x = 3:
y = -|3| = -3
Now, we can plot these points on a graph. We'll plot the x-values on the horizontal axis (x-axis) and the y-values on the vertical axis (y-axis):
(-3, -3), (-2, -2), (-1, -1), (0, 0), (1, -1), (2, -2), (3, -3)
The resulting graph should resemble a "V" shape, symmetric about the y-axis.
To graph the equation y = –|x|, we can follow these steps using integer values of x from -3 to 3:
1. Start by listing the values of x from -3 to 3:
x = -3, -2, -1, 0, 1, 2, 3
2. Substitute each value of x into the equation to find the corresponding y-values:
For x = -3, y = -|-3| = -3
For x = -2, y = -|-2| = -2
For x = -1, y = -|-1| = -1
For x = 0, y = -|0| = 0
For x = 1, y = -|1| = -1
For x = 2, y = -|2| = -2
For x = 3, y = -|3| = -3
3. Plot each point (x, y) on a graph, labeling both axes:
The points (-3, -3), (-2, -2), (-1, -1), (0, 0), (1, -1), (2, -2), and (3, -3) should be plotted.
4. Draw a line connecting the points on the graph. Since the equation is y = -|x|, the line will be V-shaped, with the vertex of the V at the origin (0, 0).
The graph of the equation y = –|x| using integer values of x from -3 to 3 would look like:
```
^
4 |
|
3 | ○
| /
2 | /
|
1 -.
| -○
0 |
|
-1 -.
| -○
-2 | \
| \
-3 | ○
+----------------->
-3 -2 -1 0 1 2 3
```
In the graph, the open circles represent the points (-3, -3), (-2, -2), (-1, -1), (1, -1), (2, -2), and (3, -3), while the filled circle represents the point (0, 0).