Key features of graphs
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What are the 'key features' of a graph?
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All Flashcards in Topic 2.4
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2.4.110 cards
What are the 'key features' of a graph?
Intercepts, maximum/minimum points, asymptotes, increasing/decreasing intervals, symmetry, and behaviour as x → ±∞.
What is a 'zero' of a function?
An x-intercept — a value of x where f(x) = 0 (also called a root).
y-intercept vs x-intercept?
y-intercept: set x = 0. x-intercept (zero/root): set y = 0.
Maximum POINT vs VALUE vs where it occurs?
Point = coordinates (a, b); value = the y-coordinate b; 'where' = the x-coordinate a. Read the question.
Local vs global maximum?
Local = highest in its neighbourhood; global = highest over the whole graph.
What is a vertical asymptote?
A line x = a the curve shoots toward (±∞) — where a denominator is 0.
What is a horizontal asymptote?
The value y approaches as x → ±∞ (the curve levels off).
What does 'increasing' mean?
As x increases, y increases — the graph goes up from left to right.
Where is y = x² increasing / decreasing?
Decreasing for x < 0, increasing for x > 0 — it turns at the vertex (x = 0).
How do you find a max/min on Paper 2?
Graph it on the GDC and use the maximum/minimum tool to read the coordinates.
2.4.29 cards
What is true at a point where two graphs meet?
It lies on both curves, so f(x) = g(x) there; the shared value is the y-coordinate.
How do you find intersections by hand?
Set f(x) = g(x), bring everything to one side, solve for x, then substitute back for y.
How do you find intersections on Paper 2?
Graph both functions on the GDC and use the intersect tool — once per crossing.
Solving f(x) = k finds where the graph meets what?
The horizontal line y = k.
Solving f(x) = 0 finds what?
The x-intercepts (zeros) — where the graph meets the x-axis.
After solving f(x) = g(x) for x, are you done?
Usually not — substitute each x back into a function to get the y-coordinate of the point.
Can two curves meet more than once?
Yes — e.g. a line can cut a parabola twice; find every crossing.
Find where y = x² + 1 meets y = 2x + 1.
x² + 1 = 2x + 1 ⇒ x² − 2x = 0 ⇒ x = 0 or 2 ⇒ (0, 1) and (2, 5).
A GDC intersect gives x = 1.52 for y = x³ − 2x and y = 1. What equation does that solve?
x³ − 2x = 1 (i.e. x³ − 2x − 1 = 0) — the intersection IS the solution.
Topic 2.4 study notes
Full notes & explanations for Key features of graphs
Math AA SL exam skills
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