Question

How do you graph `y=ln(x+1)`?

Answer 1

Shift the graph of `ln(x)` to the left by `1`

Explanation:

graph{ln(x+1) [-5, 5, -5, 5]}

Remember that since `ln(x)` and `e^x` are inverse functions `ln(e^x)=x`.

Because if `y=ln(x)` then `y=0` if and only if `ln(x)=0`. Since `e^0=1` then `ln(e^0)=ln(1)=0.` So when we change the function to `y=ln(x+1)`, we have that `y=0=ln(1)=ln(0+1)` So the x-intercept shifts to the left. Just like the x-intercept shift, the entire graph shifts to the left.