Practice Flashcards
How do you draw y = |f(x)| from y = f(x)?
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All Flashcards in Topic 2.16
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2.16.18 cards
How do you draw y = |f(x)| from y = f(x)?
Reflect any part below the x-axis up above it; leave the rest unchanged.
How do you draw y = f(|x|) from y = f(x)?
Keep the graph for x ≥ 0 and reflect it across the y-axis (the left half is discarded).
How do you draw y = 1/f(x)?
Take reciprocals of the heights: zeros of f → vertical asymptotes; large f → near 0; max ↔ min; sign kept.
Where does y = 1/f(x) have a vertical asymptote?
Wherever f(x) = 0.
Is y = f(|x|) always symmetric?
Yes — it's symmetric in the y-axis (an even function).
y = |2x − 4|: shape and minimum?
A V with vertex (2, 0); minimum value 0.
What happens to a maximum of f under y = 1/f(x)?
It becomes a minimum of 1/f (with the same sign).
Difference between |f(x)| and f(|x|)?
|f(x)| reflects below-axis parts up; f(|x|) mirrors the right half across the y-axis.
2.16.28 cards
How do you solve |inside| = c?
Set inside = +c and inside = −c (provided c ≥ 0), and solve both.
What does |x| < a mean?
−a < x < a (a band around 0).
What does |x| > a mean?
x < −a or x > a (everything outside the band).
Can |something| equal a negative number?
No — a modulus is always ≥ 0, so |…| = (negative) has no solution.
Solve |2x − 1| = 5.
2x − 1 = ±5 ⇒ x = 3 or x = −2.
Solve |x − 2| < 3.
−3 < x − 2 < 3 ⇒ −1 < x < 5.
How do you solve |f(x)| = |g(x)|?
f = g or f = −g (or square both sides).
Solve |2x + 1| ≥ 4.
2x + 1 ≥ 4 or ≤ −4 ⇒ x ≥ 3/2 or x ≤ −5/2.
Topic 2.16 study notes
Full notes & explanations for Modulus functions (HL only)
Math AA exam skills
Paper structures, command terms & tips
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