Rational Expressions and Functions flashcards

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In Rational Expressions and Excluded Values, what does original denominator mean?Rational Expressions and Excluded Values: A polynomial ratio and its domain restriction.
Why check the original denominator first?Rational Expressions and Excluded Values: Cancellation can hide a forbidden input.
In Rational Expressions and Excluded Values, what does factoring and cancellation mean?Rational Expressions and Excluded Values: Reduction of a rational expression on its valid domain.
Can a cancelled input be added back to the domain?Rational Expressions and Excluded Values: No, the original expression was undefined there.
In Rational Expressions and Excluded Values, what does equivalent restricted rules mean?Rational Expressions and Excluded Values: Equality of rational formulas under stated restrictions.
What creates a hole?Rational Expressions and Excluded Values: A cancelled denominator factor leaves its original input excluded.
In Multiplying and Dividing Rational Expressions, what does multiplication mean?Multiplying and Dividing Rational Expressions: The product of two polynomial fractions.
What must be tracked before canceling?Multiplying and Dividing Rational Expressions: All inputs excluded by the original denominators.
In Multiplying and Dividing Rational Expressions, what does division and reciprocals mean?Multiplying and Dividing Rational Expressions: Rational division as multiplication by a reciprocal.
Why exclude a zero divisor?Multiplying and Dividing Rational Expressions: Division by zero is undefined.
In Multiplying and Dividing Rational Expressions, what does checking a product mean?Multiplying and Dividing Rational Expressions: A diagnostic substitution for a rational identity.
Can substitution alone prove equality for every input?Multiplying and Dividing Rational Expressions: No, also justify the factor algebra.
In Adding and Subtracting Rational Expressions, what does least common denominator mean?Adding and Subtracting Rational Expressions: A denominator divisible by each original denominator.
Why factor before choosing it?Adding and Subtracting Rational Expressions: Factoring reveals shared factors and avoids needless multiplication.
In Adding and Subtracting Rational Expressions, what does equivalent numerators mean?Adding and Subtracting Rational Expressions: A fraction rewrite preserving value on its domain.
Why not add denominators directly?Adding and Subtracting Rational Expressions: Addition combines numerators over a shared denominator.
In Adding and Subtracting Rational Expressions, what does final simplification mean?Adding and Subtracting Rational Expressions: A simplified sum with a preserved domain.
Why keep restrictions after cancellation?Adding and Subtracting Rational Expressions: An originally undefined input stays invalid.
In Graphing Rational Functions, what does vertical asymptotes mean?Graphing Rational Functions: A vertical line approached near a nonremovable pole.
How is a hole different?Graphing Rational Functions: A hole comes from a cancelled common factor.
In Graphing Rational Functions, what does horizontal asymptotes mean?Graphing Rational Functions: A horizontal line approached at extreme inputs.
Must a graph avoid crossing a horizontal asymptote?Graphing Rational Functions: No, other rational functions can cross one.
In Graphing Rational Functions, what does holes and intercepts mean?Graphing Rational Functions: Valid intercepts and removable discontinuities.
Can an excluded x be an x-intercept?Graphing Rational Functions: No, the function has no output there.
In Rational Equations and Variation, what does solving rational equations mean?Rational Equations and Variation: An equation involving rational expressions and domain checks.
Why can clearing denominators add invalid candidates?Rational Equations and Variation: Multiplication by an expression zero at an excluded input is not reversible there.
In Rational Equations and Variation, what does direct variation mean?Rational Equations and Variation: A constant ratio between two quantities.
What does k represent?Rational Equations and Variation: The constant of proportionality.
In Rational Equations and Variation, what does inverse variation mean?Rational Equations and Variation: A constant product relationship.
Can x=0 be used in y=k/x?Rational Equations and Variation: No, division by zero is undefined.