Graphing Calculator

Linear functions (y = mx + b) produce straight lines. Quadratic functions (y = ax^2 + bx + c) create parabolas. Cubic and higher-degree polynomials generate curves with multiple bends. Trigonometric functions like sin(x) and cos(x) produce periodic waves. Exponential functions (y = a^x) model growth and decay, while logarithmic functions (y = log(x)) are their inverses. Each type has characteristic shapes that help you quickly identify them on a graph.

Roots (zeros) are where a function crosses the x-axis — the values of x where f(x) = 0. Intersections are where two functions have the same value — the points where their graphs cross. Both are fundamental in algebra and calculus. You can find them visually by plotting the functions and looking for crossing points, or algebraically by setting the equations equal and solving.

Start with a standard window (-10 to 10 on both axes) and adjust from there. If you can't see the interesting parts of the graph, zoom out. If the graph looks like a straight line when it shouldn't, zoom in. When comparing functions, plot them in different colors on the same axes. For trigonometric functions, use a window that shows at least one complete period — typically -2pi to 2pi for sine and cosine.