To find the new equation after translating the function, we need to follow two basic translation rules for functions.
1. **Translation to the Left**: When we translate a function horizontally to the left by ‘h’ units, we replace ‘x’ with ‘x + h’ in the equation. In this case, we are translating 3 units to the left, so we replace ‘x’ with ‘x + 3’.
2. **Translation Upwards**: To translate a function vertically upwards by ‘k’ units, we simply add ‘k’ to the entire function. Here, we are translating 4 units up. So, we will add 4 to the new equation.
Starting with the original function:
y = 2x
After translating 3 units to the left, we have:
y = 2(x + 3)
Now, expanding this gives us:
y = 2x + 6
Next, we translate this function 4 units up:
y = 2x + 6 + 4
Which simplifies to:
y = 2x + 10
Thus, the equation of the function after translating it 3 units to the left and 4 units up is:
y = 2x + 10