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Power Function Calculator

Online power function calculator: enter the exponent α and argument x to evaluate y=x^α, and compare common power functions (linear, quadratic, cubic, square root, reciprocal). It is the basis for understanding growth and graphs.

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y = x^α
xx²√x
Constant, e.g. 2, 1/2, −1
Usually positive x>0

📖 Tutorial | Power Function

1. Definition
A function of the form y=x^α (α constant) is a power function; the base is the variable and the exponent is constant. Distinguish it from the exponential y=a^x.
2. Formula & Notation
xVariable (base)
αConstant exponent
yx^α
3. Properties & Laws
  • Every power function passes through (1,1);
  • α=1 a line, 2 a parabola, 3 a cubic;
  • α=1/2 the square root, α=−1 the reciprocal;
  • For α>0 it passes the origin and rises in quadrant I;
  • For α<0 it falls with the axes as asymptotes.
4. Steps
  1. Enter the exponent α and base x;
  2. Click "Calculate" for y;
  3. Or click "Load Example".
5. Worked Examples
Example: y=x² at x=3 gives 9; α=1/2, x=16 gives √16=4.
6. Common Pitfalls
The exponent is constant — do not confuse with the exponential function;
Fractional exponents are roots, negative exponents reciprocals;
Graphs are usually studied for x>0.

❓ FAQ | Power Function

What is a power function?
y=x^α with constant α; not y=a^x.
Common point?
(1,1), since 1 to any power is 1.
Sign of α?
α>0 rises through the origin; α<0 falls toward the axes.
Common ones?
x, x², x³, √x, 1/x.
Fractional exponent?
x^(1/n)=ⁿ√x.
Domain of x?
Usually x>0; even roots need non-negative.