Practice Flashcards
Flip to reveal answersWhat is true at a point where two graphs meet?
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All 9 Flashcards — GDC intersections
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Question
What is true at a point where two graphs meet?
Answer
It lies on both curves, so f(x) = g(x) there; the shared value is the y-coordinate.
Question
How do you find intersections by hand?
Answer
Set f(x) = g(x), bring everything to one side, solve for x, then substitute back for y.
Question
How do you find intersections on Paper 2?
Answer
Graph both functions on the GDC and use the intersect tool — once per crossing.
Question
Solving f(x) = k finds where the graph meets what?
Answer
The horizontal line y = k.
Question
Solving f(x) = 0 finds what?
Answer
The x-intercepts (zeros) — where the graph meets the x-axis.
Question
After solving f(x) = g(x) for x, are you done?
Answer
Usually not — substitute each x back into a function to get the y-coordinate of the point.
Question
Can two curves meet more than once?
Answer
Yes — e.g. a line can cut a parabola twice; find every crossing.
Question
Find where y = x² + 1 meets y = 2x + 1.
Answer
x² + 1 = 2x + 1 ⇒ x² − 2x = 0 ⇒ x = 0 or 2 ⇒ (0, 1) and (2, 5).
Question
A GDC intersect gives x = 1.52 for y = x³ − 2x and y = 1. What equation does that solve?
Answer
x³ − 2x = 1 (i.e. x³ − 2x − 1 = 0) — the intersection IS the solution.
Read the notes
Full study notes for GDC intersections
Topic 2.4 hub
Key features of graphs
More from Topic 2.4
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Math AA SL exam skills
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