Rational Functions and Zeros

The zeros of rational functions are the values of x that make the numerator equal to zero, provided they are in the domain.

Functions30–40% of exam

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Context

What this topic is and why it exists

Rational functions are expressions where one polynomial is divided by another.

To find the zeros of a rational function, you focus on the numerator: set it equal to zero and solve.

The zeros of the numerator correspond to the zeros of the rational function, provided these values aren't also zeros of the denominator.

If the denominator is zero at the same point, you get a hole instead of a zero.

This is where it gets tricky: distinguishing between zeros and holes requires precise attention to both numerator and denominator.

The numerator gives potential zeros, but the denominator can negate them, turning them into undefined points or holes.

Misidentifying a hole as a zero is a common mistake.

It happens when you forget to check if a zero of the numerator is also a zero of the denominator.

That oversight means misreading the function's graph and behavior, leading to incorrect conclusions about continuity and intercepts.

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