Practice Flashcards
How do you solve f(x) ≥ g(x) graphically?
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All Flashcards in Topic 2.15
Below are all 8 flashcards for this topic. Sign up free to track your progress and get personalized review schedules.
2.15.18 cards
How do you solve f(x) ≥ g(x) graphically?
Find the intersections (f = g); they bound the intervals where f is on or above g.
How do you solve an inequality analytically?
Move everything to one side, find zeros and undefined points, then do a sign analysis on a number line.
Why not cross-multiply a rational inequality?
The denominator could be negative, which would flip the inequality direction.
Where is an upward parabola positive?
Outside its roots (x < smaller or x > larger); negative between them.
Solve x² ≤ x + 2.
Roots of x² = x + 2 are −1, 2; the parabola is below the line between them: −1 ≤ x ≤ 2.
Solve (x − 1)/(x + 2) ≥ 0.
Critical points 1 (zero), −2 (undefined); sign analysis gives x < −2 or x ≥ 1.
Do you include the endpoints?
Yes for ≤/≥ — except any x that makes a denominator zero (always excluded).
What are the 'critical points' of a rational inequality?
Where the expression is zero (numerator = 0) or undefined (denominator = 0).
Topic 2.15 study notes
Full notes & explanations for Inequalities (HL only)
Math AA exam skills
Paper structures, command terms & tips
Want smart review reminders?
Sign up free to track your progress. Our spaced repetition algorithm will tell you exactly which cards to review and when.
Start Free