Unit 7: Rational Functions - Review 12/6/24
Flashcard
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Mathematics
•
11th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is a rational function?
Back
A rational function is a function that can be expressed as the quotient of two polynomials, typically in the form f(x) = P(x)/Q(x), where P and Q are polynomials.
2.
FLASHCARD QUESTION
Front
What does it mean to simplify a rational function?
Back
Simplifying a rational function involves factoring the numerator and denominator, canceling out common factors, and rewriting the function in its simplest form.
3.
FLASHCARD QUESTION
Front
How do you factor a polynomial?
Back
To factor a polynomial, you look for common factors, use techniques like grouping, or apply special formulas such as the difference of squares or the quadratic formula.
4.
FLASHCARD QUESTION
Front
What is the significance of canceling factors in rational functions?
Back
Canceling factors in rational functions helps to simplify the expression, making it easier to analyze, graph, or compute limits.
5.
FLASHCARD QUESTION
Front
What is the vertical asymptote of a rational function?
Back
A vertical asymptote occurs at values of x that make the denominator zero (Q(x) = 0) and are not canceled out by the numerator.
6.
FLASHCARD QUESTION
Front
What is the horizontal asymptote of a rational function?
Back
The horizontal asymptote describes the behavior of the function as x approaches infinity. It can be determined by comparing the degrees of the numerator and denominator.
7.
FLASHCARD QUESTION
Front
How do you find the x-intercepts of a rational function?
Back
To find the x-intercepts, set the numerator equal to zero (P(x) = 0) and solve for x.
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