Bot Graph the equation by translating y = |x|.
y = |x + 7|
To graph the equation y = |x + 7|, we need to understand the properties of absolute value functions and how they affect the graph.
1. Start by identifying the vertex of the absolute value function. In this case, the vertex is at (-7, 0), which corresponds to the value within the absolute value.
2. The vertex gives us a starting point. From there, we can analyze the behavior of the absolute value function on either side of the vertex.
3. For x ≤ -7, the expression x + 7 is negative, so the absolute value function becomes -x - 7.
4. For x > -7, the expression x + 7 is positive, so the absolute value function remains as x + 7.
5. Now, plot a few points to sketch the graph. Choose x-values on either side of -7, such as x = -8, -7, -6, -5. Calculate the corresponding y-values for each point.
For x = -8, y = -(-8) - 7 = 1
For x = -7, y = 0
For x = -6, y = -(-6) - 7 = -1
For x = -5, y = -(-5) - 7 = -2
6. Plot these points on a graph and connect them with a line. Reflect the portion of the graph for x ≤ -7 across the vertex (-7, 0) to complete the graph.
Here is the graph of y = |x + 7|:
```
1__
| \
| \
| \
| \
____________|____\____________
-7 0
```
The graph starts at (-7, 0) and splits into two branches. One branch extends upwards while the other branch extends downwards, forming a "V" shape with the vertex at (-7, 0).