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## Inverse of a function

**Horizontal Line Test (水平線測試) :** Test if a function is a one-to-one function.

If a horizontal line crosses a graph more than once, the graph is not the graph of a one-to-one function. Thus the function is not invertible. (不可逆的函數)

1. Press the play icon on the bottom-left and watch the animation.

2. You can change the function by typing the function, f(x)=..., in the input bar and playing again.

3. If a function is a not one-to-one function, we can restrict the domain and make it invertible. Right click on f(x), then change Function[x³ + 2 x² + 1, -∞, ∞] to Function[x³ + 2 x² + 1, 0, ∞]. Do the test again.

**Inverse of a function (逆函數):**
Find the graph of an inverse function interactively. In this worksheet, students will discover the relation between the graph of a function and the graph of its inverse, and discover the relationship between the domains and ranges of each.

Graph of a Function and its Inverse worksheet

By Vera Hu-Hyneman