Transformations of Rational Functions

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•
Mathematics
•
10th - 12th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a vertical asymptote?
Back
A vertical asymptote is a line x = a where a rational function approaches infinity or negative infinity as the input approaches a. It indicates values that the function cannot take.
2.
FLASHCARD QUESTION
Front
What are the asymptotes of the function g(x) = 4 / (x - 5)?
Back
The asymptotes are x = 5 (vertical asymptote) and y = 0 (horizontal asymptote).
3.
FLASHCARD QUESTION
Front
What is a horizontal asymptote?
Back
A horizontal asymptote is a line y = b that a function approaches as x approaches infinity or negative infinity. It indicates the end behavior of the function.
4.
FLASHCARD QUESTION
Front
What transformation occurs when the function g(x) = 1/x is shifted right by 5 units?
Back
The new function is g(x) = 1/(x - 5).
5.
FLASHCARD QUESTION
Front
What transformation occurs when the function g(x) = 1/x is shifted up by 7 units?
Back
The new function is g(x) = 1/x + 7.
6.
FLASHCARD QUESTION
Front
What does it mean to reflect a function over the x-axis?
Back
Reflecting a function over the x-axis means to multiply the function by -1, changing the sign of the output values.
7.
FLASHCARD QUESTION
Front
How do you determine the vertical asymptote of a rational function?
Back
Set the denominator equal to zero and solve for x. The values of x that make the denominator zero are the vertical asymptotes.
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