Draw the graph of the following inverse trigonometric function arctan x.

To graph the inverse trigonometric function arctan(x), you can follow these steps:

Understanding the Function

The function arctan(x) gives the angle whose tangent is x. Its range is from -π/2 to π/2, and it is defined for all real numbers.

Key Features of the Graph

• Asymptotes: The graph approaches y = -π/2 as x approaches negative infinity and y = π/2 as x approaches positive infinity.
• Intercept: The graph crosses the origin at the point (0, 0).
• Increasing Function: The function is always increasing, meaning as x increases, arctan(x) also increases.

Steps to Draw the Graph

1. Start by plotting the intercept at (0, 0).
2. Draw horizontal dashed lines to represent the asymptotes at y = -π/2 and y = π/2.
3. Sketch the curve starting from the left, approaching y = -π/2 as x goes to negative infinity.
4. Continue the curve, passing through (0, 0), and approaching y = π/2 as x goes to positive infinity.

Final Thoughts

By following these steps, you can create an accurate graph of the arctan(x) function, showcasing its unique properties and behavior.