Graphs of |f(x)|, f(|x|) and 1/f(x)
Practice Flashcards
Flip to reveal answersHow do you draw y = |f(x)| from y = f(x)?
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All 8 Flashcards — Graphs of |f(x)|, f(|x|) and 1/f(x)
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Question
How do you draw y = |f(x)| from y = f(x)?
Answer
Reflect any part below the x-axis up above it; leave the rest unchanged.
Question
How do you draw y = f(|x|) from y = f(x)?
Answer
Keep the graph for x ≥ 0 and reflect it across the y-axis (the left half is discarded).
Question
How do you draw y = 1/f(x)?
Answer
Take reciprocals of the heights: zeros of f → vertical asymptotes; large f → near 0; max ↔ min; sign kept.
Question
Where does y = 1/f(x) have a vertical asymptote?
Answer
Wherever f(x) = 0.
Question
Is y = f(|x|) always symmetric?
Answer
Yes — it's symmetric in the y-axis (an even function).
Question
y = |2x − 4|: shape and minimum?
Answer
A V with vertex (2, 0); minimum value 0.
Question
What happens to a maximum of f under y = 1/f(x)?
Answer
It becomes a minimum of 1/f (with the same sign).
Question
Difference between |f(x)| and f(|x|)?
Answer
|f(x)| reflects below-axis parts up; f(|x|) mirrors the right half across the y-axis.
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Full study notes for Graphs of |f(x)|, f(|x|) and 1/f(x)
Topic 2.16 hub
Modulus functions (HL only)
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