To find the equation of the function y = 2x after it has been translated, we need to follow a couple of simple steps. Translations in the coordinate plane can be expressed mathematically by adjusting the function in the following ways:
1. **Translating Left/Right**: To translate a function to the left, you subtract from the x-value. For a translation of 3 units to the left, we replace x with (x + 3).
2. **Translating Up/Down**: To translate a function up, we add to the entire function. For a translation of 4 units up, we add 4 to the function itself.
Now, let’s apply these transformations to the original equation:
Starting with the original function:
y = 2x
First, we translate it 3 units to the left:
y = 2(x + 3)
Next, we simplify this:
y = 2x + 6
Now, we translate it 4 units up by adding 4 to the entire function:
y = 2x + 6 + 4
Simplifying gives us:
y = 2x + 10
So, the equation of the function y = 2x translated 3 units to the left and 4 units up is:
y = 2x + 10