Function Zoo

Algebra 2 · Axiom Academy

Explore different function families as exotic creatures, each with unique behaviors and habitats. Just like animals come in different species with unique traits, functions belong to different families with distinct behaviors. Four of them live here, and once you know the family you can predict what a function will do long before you plot a single point. Meet the residents: the Linear Giraffe f(x) = mx + b , the Quadratic Kangaroo f(x) = ax^2 + bx + c , the Exponential Cheetah , and the Logarithmic Tortoise . Turn all four loose on the same track and press play. The sweep line walks x from 0 to 5, and each creature draws its own path as it goes — watch who is ahead, who gets passed, and who is simply not in the same league. Habitat note: each function lives in its own domain — the x -values where it is defined and happy. At x = 0 the Cheetah already stands at 1 while the others are still at 0, and the Tortoise does not exist at all: its readout is a dash, because you cannot take a logarithm of zero or of a negative number. The Linear Giraffe: Steady and Straight The Linear Giraffe walks in perfectly straight lines. Its path never curves — just constant, predictable motion. Drag the sliders and watch the stride ladder beside the graph: every time x takes one step to the right, the height changes by exactly m . The same amount. Every single time.

This is the written version of the interactive lesson above. See the full Algebra 2 course.