Reciprocal function in basic maths 
Show example graphs with steps

The graph above illustrates the reciprocal function \( f(x) = \frac{1}{x} \):

- The vertical asymptote (red dashed line) is at \( x = 0 \), where the function is undefined.
- The horizontal asymptote (green dashed line) is at \( y = 0 \), where the function approaches zero as \( x \) becomes very large or very small.

### Summary of Steps:
1. Identify key points on the graph, such as \( f(1) = 1 \) and \( f(-1) = -1 \).
2. Draw the vertical asymptote at \( x = 0 \) and the horizontal asymptote at \( y = 0 \).
3. Sketch the curve, ensuring that the function gets very large near \( x = 0 \) and approaches zero for large \( x \) values.

Would you like any further details, or do you have questions?

Here are 5 related questions for you:
1. How does the reciprocal function change when a constant is added?
2. What happens to the graph of \( f(x) = \frac{1}{x} \) if the reciprocal is squared?
3. How do reciprocal functions relate to hyperbolas?
4. Can you give an example of a real-world application of reciprocal functions?
5. How do you find the inverse of a reciprocal function?

**Tip**: When graphing functions, understanding asymptotes helps predict the behavior at critical points.

Reciprocal function in basic maths. Show example graphs with steps.

Understand the reciprocal function f(x) = 1/x by learning how to graph it step by step. This guide explains the behavior of vertical and horizontal asymptotes and provides key points like f(1) = 1 and f(-1) = -1. Ideal for students in Grades 8-10.

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