Project 2: The Visual Graphing Calculator

Build a graphing tool that plots functions and highlights key features.

Project Overview

Attribute Value
Difficulty Level 1: Beginner
Time Estimate Weekend
Main Language Python
Alternative Languages JavaScript, C++
Knowledge Area Functions and graphs
Tools Matplotlib or simple plotting
Main Book “Precalculus” by James Stewart

What you’ll build: A tool that plots functions like y = x^2 and marks intercepts, maxima, and minima.

Why it teaches math: Graphs make abstract equations visible, and key features reveal how functions behave.

Core challenges you’ll face:

  • Sampling functions accurately
  • Identifying intercepts and turning points
  • Scaling axes for readability

Real World Outcome

You will type in a function and see a plotted graph with labeled key points.

Example Output:

$ python graph.py "x**2 - 4"
Plotted function over [-10, 10]
Intercepts: x = -2, 2
Minimum at x = 0, y = -4

Verification steps:

  • Compare to textbook graphs
  • Confirm key points by hand

The Core Question You’re Answering

“How do I turn a formula into a picture that reveals its behavior?”

Graphing makes function behavior intuitive.

Concepts You Must Understand First

Stop and research these before coding:

  1. Function evaluation
    • What does it mean to plug a value into a function?
    • Book Reference: “Precalculus” by James Stewart, Ch. 2
  2. Intercepts and roots
    • How do you find where a graph crosses axes?
    • Book Reference: “Precalculus” by James Stewart, Ch. 3
  3. Turning points
    • How do you identify maxima and minima visually?
    • Book Reference: “Precalculus” by James Stewart, Ch. 3

Questions to Guide Your Design

  1. Sampling
    • How many points do you need for a smooth curve?
    • How will you handle discontinuities?
  2. Feature detection
    • Will you approximate derivatives numerically?
    • How will you avoid false turning points from noise?

Thinking Exercise

Plot a Parabola

Sketch y = x^2 - 4 and mark its intercepts and vertex.

Questions while working:

  • Where does the curve cross the x-axis?
  • How does the coefficient change the width?

The Interview Questions They’ll Ask

Prepare to answer these:

  1. “How do you find intercepts from an equation?”
  2. “What does the vertex of a parabola represent?”
  3. “How do you choose a graphing window?”
  4. “What is a turning point?”
  5. “How do you detect discontinuities?”

Hints in Layers

Hint 1: Starting Point Start by plotting sample points without annotations.

Hint 2: Next Level Detect sign changes to approximate roots.

Hint 3: Technical Details Use numerical derivatives to estimate turning points.

Hint 4: Tools/Debugging Compare output with known graphs from a textbook.

Books That Will Help

Topic Book Chapter
Function graphs “Precalculus” by James Stewart Ch. 2
Intercepts “Precalculus” by James Stewart Ch. 3
Turning points “Precalculus” by James Stewart Ch. 3

Implementation Hints

  • Start with polynomial functions only.
  • Make axis scaling configurable.
  • Label key points clearly on the plot.

Learning Milestones

  1. First milestone: You can plot basic functions reliably.
  2. Second milestone: You can detect and label intercepts.
  3. Final milestone: You can identify maxima and minima accurately.