LearnViz CompSci
Home / Learn / Math for Computing / Functions and Graphs

Beginner Topic 5 of 51 Math for Computing

Functions and Graphs

Visualizing relationships between quantities.

How it works

A function assigns each input in its domain exactly one output in its range, and its graph plots the input-output pairs. Key families are linear, quadratic and polynomial, exponential and logarithmic, trigonometric and piecewise functions. Properties include domain and range, intercepts, increasing or decreasing behavior, symmetry, asymptotes, continuity and transformations such as shifts, stretches and reflections. Composition and inverses combine and undo functions.

Where it is used

Plotting data, modeling relationships, analyzing growth rates of algorithms, activation functions in neural networks and defining mappings in programs use functions and graphs.

Common pitfall

Confusing a function with its formula ignores domain restrictions, such as division by zero. The vertical line test is needed to see if a curve is a function. Wrong scales, such as linear instead of log axes, hide behavior. Composition order matters: f of g is not g of f. Sketch graphs, check special points and test values on both sides of critical points.

Where it fits in the course

Functions and Graphs is topic 5 of 51 in Math for Computing, rated Beginner. It follows Summations and Series. The next topic is Vectors.

Practice and explore

How to study this topic

  1. Read the explanation above and restate the definition in your own words.
  2. Open the interactive lesson and answer its mini quiz.
  3. Read the common pitfall, then write a short example that avoids it.
  4. Check your understanding in the Math for Computing quiz, and revisit the topic if you miss a question.

Frequently asked questions

What is Functions and Graphs?
Visualizing relationships between quantities. It belongs to Math for Computing and is a beginner-level topic.
Where do people use Functions and Graphs?
Plotting data, modeling relationships, analyzing growth rates of algorithms, activation functions in neural networks and defining mappings in programs use functions and graphs.
What is the most common mistake with Functions and Graphs?
Confusing a function with its formula ignores domain restrictions, such as division by zero.
What should I learn before this topic?
Start with Summations and Series, the topic just before it in Math for Computing.
How can I practice it?
Answer the mini quiz in the interactive lesson, then take the Math for Computing quiz. You can also explore Graph Traversal in the Visual Lab.
Is Functions and Graphs hard to learn?
It is a Beginner topic, so it works as an entry point. If the terms are new, read the explanation twice and try the visualizer before the quiz.
How long does it take to learn Functions and Graphs?
Most learners can read the explanation and finish the interactive lesson in under an hour. Fluency comes from applying the idea, so plan a few short practice sessions with the quiz.
Which topics are related to Functions and Graphs?
Summations and Series, Vectors, Exponents and Logarithms are closely connected. The full list is in the related topics section of this page.
What should I study after Functions and Graphs?
Continue with Vectors, the next topic in Math for Computing.

Related topics