Question

How to sketch the graph for `y=10^(x) -1` ?

Answer 1

See below.

Explanation:

Take a look at a sample graph of an exponential function:

graph{e^x [-10, 10, -5, 5]}

This is `y=e^x` by the way, and how I typically visualise exponential function graphs.

We'll start with the graph of `10^x`. The `x` axis is a horizontal asymptote "at negative infinity" for exponential functions like this. Notice how the graph is different with a greater base. `e` is about `2.7`, while in our case we have `10` as base.

graph{10^x [-10, 10, -5, 5]}

To get `10^x-1`, you'll have to shift that entire graph downwards `1` unit:

graph{10^x-1 [-10, 10, -5, 5]}