Graphs of functions
Cambridge IGCSE Mathematics (0580) · Unit 2: Algebra and graphs · 9 flashcards
Graphs of functions is topic 2.6 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 2 — Algebra and graphs , alongside Algebraic notation and manipulation, Equations and Inequalities. In one line: The origin is the point where the x-axis and y-axis intersect. Its coordinates are (0, 0).
This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator.
The deck below contains 9 flashcards — 4 definitions, 4 key concepts and 1 application card — covering the precise wording mark schemes reward. Use the 4 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.
The coordinates of the origin
The origin is the point where the x-axis and y-axis intersect. Its coordinates are (0, 0).
Questions this Graphs of functions deck will help you answer
- › Sketch the general shape of a quadratic graph. What is its equation form?
- › What is the shape of a reciprocal graph and what is its equation?
- › Describe the general shape of an exponential graph, where y=a^x and a > 1.
- › Describe the general shape of a cubic graph.
- › Explain how to plot the graph of y = 2x + 1.
What are the coordinates of the origin?
The origin is the point where the x-axis and y-axis intersect. Its coordinates are (0, 0).
Sketch the general shape of a quadratic graph. What is its equation form?
A quadratic graph is a parabola (U-shaped). The general form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants.
What is the shape of a reciprocal graph and what is its equation?
A reciprocal graph has two curves, approaching the x and y axis but never touching them. Its equation form is y = k/x, where k is a constant.
What is an asymptote? Give an example in the context of graphs.
An asymptote is a line that a curve approaches but never touches.
Describe the general shape of an exponential graph, where y=a^x and a > 1.
An exponential graph rises rapidly as x increases and approaches the x-axis as x decreases. It always passes through the point (0,1) and has the x-axis (y=0) as an asymptote.
Describe the general shape of a cubic graph.
A cubic graph generally has an 'S' shape or a similar wavy form. Its equation form is y = ax³ + bx² + cx + d, where a, b, c, and d are constants.
What is the x-intercept of a graph? How do you find it?
The x-intercept is the point where the graph crosses the x-axis. To find it, set y = 0 in the equation and solve for x.
What is the y-intercept of a graph? How do you find it?
The y-intercept is the point where the graph crosses the y-axis. To find it, set x = 0 in the equation and solve for y.
Explain how to plot the graph of y = 2x + 1.
Create a table of values for x and y. For each x-value, calculate the corresponding y-value using the equation. Then, plot the points (x, y) on a coordinate plane and draw a straight line through them.
Key Questions: Graphs of functions
What are the coordinates of the origin?
The origin is the point where the x-axis and y-axis intersect. Its coordinates are (0, 0).
What is an asymptote? Give an example in the context of graphs.
An asymptote is a line that a curve approaches but never touches.
What is the x-intercept of a graph? How do you find it?
The x-intercept is the point where the graph crosses the x-axis. To find it, set y = 0 in the equation and solve for x.
What is the y-intercept of a graph? How do you find it?
The y-intercept is the point where the graph crosses the y-axis. To find it, set x = 0 in the equation and solve for y.
Tips to avoid common mistakes in Graphs of functions
- ● When calculating a gradient, carefully consider the scale of each axis; the gradient is the change in y divided by the change in x, considering the respective scale.
- ● Use brackets around composite function substitutions, like f(x – 2) = 3(x – 2)^2 + 1.
More topics in Unit 2 — Algebra and graphs
Graphs of functions sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.
Cambridge syllabus keywords to use in your answers
These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.
Key terms covered in this Graphs of functions deck
Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.
Related Mathematics guides
Long-read articles that go beyond the deck — cover the whole subject's common mistakes, high-yield content and revision pacing.
How to study this Graphs of functions deck
Start in Study Mode, attempt each card before flipping, then rate Hard, Okay or Easy. Cards you rate Hard come back within a day; cards you rate Easy push out to weeks. Your progress is saved in your browser, so come back daily for 5–10 minute reviews until every card reads Mastered.
Study Mode
Space to flip • ←→ to navigate • Esc to close
You're on a roll!
You've viewed 10 topics today
Create a free account to unlock unlimited access to all revision notes, flashcards, and study materials.
You're all set!
Enjoy unlimited access to all study materials.
Something went wrong. Please try again.
What you'll get:
- Unlimited revision notes & flashcards
- Track your study progress
- No spam, just study updates