Rational function inequalities (HSC SSCE Mathematics Extension 1): Flashcards
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What is a rational function?
What is a rational function?
A function dividing one polynomial by another.
Why are undefined points important?
Why are undefined points important?
They affect intervals in inequality analysis.
How do you find undefined points?
How do you find undefined points?
Set the denominator to zero.
What are critical points in rational functions?
What are critical points in rational functions?
Points where the function is undefined or crosses x-axis.
What is the first step in solving inequalities?
What is the first step in solving inequalities?
Isolate the variable on one side of the inequality.
What methods can solve rational inequalities?
What methods can solve rational inequalities?
Graphical and algebraic methods.
How do you handle undefined points in solutions?
How do you handle undefined points in solutions?
Exclude them from the domain and solutions.
What must be considered when multiplying by a variable?
What must be considered when multiplying by a variable?
Check the sign of the variable to maintain inequality direction.
What is sign analysis in rational inequalities?
What is sign analysis in rational inequalities?
Evaluating the sign of expressions in intervals.
What should you do after finding critical points?
What should you do after finding critical points?
Verify interval signs to determine solutions.