Use the graph of 𝑦 = 𝑓(𝑥) to sketch the graph of the translation below 𝑦 = 𝑓(𝑥) − 3
To sketch the graph of 𝑦 = 𝑓(𝑥) − 3, we will start by taking the graph of 𝑦 = 𝑓(𝑥) and shift it downward 3 units.
If the original graph of 𝑦 = 𝑓(𝑥) passes through the point (𝑥₀, 𝑦₀), then the graph of 𝑦 = 𝑓(𝑥) − 3 will pass through the point (𝑥₀, 𝑦₀ − 3).
Thus, every point on the graph of 𝑦 = 𝑓(𝑥) will be shifted downward 3 units to obtain the graph of 𝑦 = 𝑓(𝑥) − 3.
Here is an example graph:
Graph of 𝑦 = 𝑓(𝑥):
|
4 | + +
| +
3 | +
| +
2 |
|
1 | +
|_______________________
-3 -2 -1 0 1 2 3
Graph of 𝑦 = 𝑓(𝑥) − 3 (shifted downward 3 units):
|
1 | + +
| +
0 | +
| +
-1 |
|
-2 | +
|_______________________
-3 -2 -1 0 1 2 3