Question

How do you graph `y>log_10(x+1)`?

Answer 1

As shown in the graph

Explanation:

The first we consider is the graph of `log_10 (x+1)` this is just `log_10(x)` undergoing the transformation of being shifted 1 to the left:

`Log_10(x)` :
graph{log(x) [-1.25, 8.75, -2.64, 2.36]}

`log_10(x+1)`: graph{log(x+1) [-2.168, 7.83, -2.62, 2.38]}

Now we must consider the inequality: Where the values of y are greater than `log_10(x+1)`, we see this must be above the function, where below the function the value of `y` is smaller than the fucntion

`=>` graph{y>log(x+1) [-2.105, 7.893, -2.3, 2.7]}

Now we see that it cuts of at `x=-1` this is due to the fucntion being underfined for `x<=-1`