Introduction to Non-Linear Functions

Linear vs quadratic vs exponential — three curves, three stories

Not every function is a straight line. A linear function like y = 2x grows at a constant rate. A quadratic like y = x^2 grows faster and faster. An exponential like y = 2^x grows faster than either — eventually it dwarfs everything else.

Understanding the difference matters in real life: a salary that grows linearly adds the same raise each year; an investment that grows exponentially doubles on a schedule; a ball thrown upward follows a quadratic path.

In this lesson, you'll see all three on one graph and discover what makes each one unique.

Related Topics

Linear EquationsQuadratic EquationsExponential Growth & Decay

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What is a non-linear function?
A non-linear function is any function whose graph is not a straight line. Quadratics (parabolas), exponentials, square roots, and trigonometric functions are all non-linear. The rate of change is not constant — it speeds up, slows down, or oscillates.
How does quadratic growth differ from linear?
A linear function adds the same amount each step (constant rate of change). A quadratic adds more and more each step — the rate of change itself increases linearly. For example, at x = 1, x² = 1; at x = 10, x² = 100; the jumps get bigger.
Why does exponential growth beat everything?
An exponential function multiplies by a constant factor each step, so it doubles, then doubles again. Eventually it overtakes any polynomial. At x = 10: 2x = 20, x² = 100, 2^x = 1024. At x = 20: 2x = 40, x² = 400, 2^x = 1,048,576.
When do I use each type of function?
Use linear for constant-rate situations (flat salary increase, constant speed). Use quadratic for acceleration (free fall, area). Use exponential for compound growth (interest, population, radioactive decay).
What can it graph?
It can plot explicit, implicit, and parametric functions, add points and geometry, and animate sliders on the same graph.
Can I use voice or a photo?
Yes. You can talk to the tutor, upload a worksheet or handwritten problem, and let the graph update from that input.
Will it explain the steps?
Yes. The AI explains what it is drawing and why, so you see the answer on the graph instead of getting only a final number.