Name: AAHL 2.13.1 Rational functions (quadratic in denominator)
Uploaded: 2025-01-04T10:03:14.160Z
Duration: 14 min
Description: Learn AAHL 2.13.1 Rational functions (quadratic in denominator) in this free IB Mathematics Analysis and Approaches (AA) video lesson for AHL 2.13—Rational functions.

The video provides a detailed lesson on sketching rational functions that involve quadratics, focusing on two main types: one with a quadratic in the denominator and another with a quadratic in the numerator.

Key steps for sketching the graph include:

Finding the x-intercepts by setting the numerator to zero, resulting in $x = 1$ .
Determining the y-intercept by evaluating the function at $x = 0$ , yielding $y = \frac{1}{6}$ .
Identifying the horizontal asymptote, which is $y = 0$ when the degree of the denominator is greater than that of the numerator.
Calculating the vertical asymptotes by solving the denominator for zero, leading to $x = -2$ and $x = 3$ .

A sign diagram is used to analyze the function's behavior across different intervals, ultimately aiding in the accurate sketching of the graph, which features key points and asymptotes.

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