Question

Draw the graph of f(x)
= 3^x

Answer 1

The function f(x) = 3ˣ is an exponential function.

Here are some steps to help you sketch the graph:

1. Select Key Points:

- Choose some key values of \(x\) and find the corresponding \(y\) values. Common choices are \(x = 0, 1, -1, 2, -2, \ldots\).

- For example:

`- \(f(0) = 3^0 = 1\)\\ - \(f(1) = 3^1 = 3\)\\ - \(f(-1) = 3^(-1) = (1)/(3)\)\\ - \(f(2) = 3^2 = 9\)\\ - \(f(-2) = 3^(-2) = (1)/(9)\)`

2. Plot Points:

- Plot the points you found on the coordinate plane.

3. Connect Points:

- Since it's an exponential function, the graph will be a smooth curve passing through the points.

4. Asymptote:

- Exponential functions have asymptotes. For
`\(f(x) = 3^x\)`, the x-axis
`(\(y = 0\))` is a horizontal asymptote because the function will get very close to, but never touch, the x-axis as x approaches negative infinity.