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Flip to reveal answersHow do you solve f(x) ≥ g(x) graphically?
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All 8 Flashcards — Solving inequalities
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Question
How do you solve f(x) ≥ g(x) graphically?
Answer
Find the intersections (f = g); they bound the intervals where f is on or above g.
Question
How do you solve an inequality analytically?
Answer
Move everything to one side, find zeros and undefined points, then do a sign analysis on a number line.
Question
Why not cross-multiply a rational inequality?
Answer
The denominator could be negative, which would flip the inequality direction.
Question
Where is an upward parabola positive?
Answer
Outside its roots (x < smaller or x > larger); negative between them.
Question
Solve x² ≤ x + 2.
Answer
Roots of x² = x + 2 are −1, 2; the parabola is below the line between them: −1 ≤ x ≤ 2.
Question
Solve (x − 1)/(x + 2) ≥ 0.
Answer
Critical points 1 (zero), −2 (undefined); sign analysis gives x < −2 or x ≥ 1.
Question
Do you include the endpoints?
Answer
Yes for ≤/≥ — except any x that makes a denominator zero (always excluded).
Question
What are the 'critical points' of a rational inequality?
Answer
Where the expression is zero (numerator = 0) or undefined (denominator = 0).
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Full study notes for Solving inequalities
Topic 2.15 hub
Inequalities (HL only)
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