Function explorer
Pick a function family, transform it with a, h, and k, and see its domain, range, intercepts, and asymptotes — or watch it converge (or diverge) at a limit.
Function family
Result
f(x) = x²
DomainAll real numbers (−∞, ∞)
Range[0, ∞)
y-intercept(0, 0)
x-intercept(s)(0, 0)
As x → −∞, f(x) → +∞. As x → +∞, f(x) → +∞.
Dashed: parent function · Solid: your transformed function
How is this calculated?
Every function here is a transformation of a parent function — the simplest member of its family. The form a·f(x − h) + k stretches or reflects it (a), shifts it sideways (h), and shifts it up or down (k). The domain and range follow directly: whatever the parent can't do (a square root can't take a negative input, a log can't take zero or less), the shift moves that restriction to x = h.
New to the math? Learn the concept: Pre-Calculus, made visual