Reciprocal function
Practice Flashcards
Flip to reveal answersWhat does the graph of y = 1/x look like?
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All 9 Flashcards — Reciprocal function
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Question
What does the graph of y = 1/x look like?
Answer
A hyperbola with two branches (top-right and bottom-left), hugging both axes.
Question
Domain and range of y = 1/x?
Answer
Domain x ≠ 0, range y ≠ 0.
Question
Asymptotes of y = 1/x?
Answer
x = 0 (vertical) and y = 0 (horizontal).
Question
How many intercepts does y = 1/x have?
Answer
None — it never reaches either axis.
Question
Asymptotes of y = 1/(x − h) + k?
Answer
Vertical x = h, horizontal y = k.
Question
Which way does 1/(x − 3) shift?
Answer
Right by 3, so the vertical asymptote is x = 3.
Question
What does the +k do in 1/(x − h) + k?
Answer
Raises the horizontal asymptote to y = k.
Question
How do you sketch a reciprocal graph?
Answer
Draw the asymptotes, find any intercepts, then draw the two branches hugging the asymptotes.
Question
Why is 1/x undefined at x = 0?
Answer
Division by zero is undefined — that's the vertical asymptote.
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Full study notes for Reciprocal function
Topic 2.8 hub
Rational functions & asymptotes
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