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Common Functions definitions

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  • Constant Function
    A rule where every input yields the same output, resulting in a horizontal line with domain all real numbers and a single-value range.
  • Identity Function
    A rule where each input equals its output, forming a straight line through the origin with both domain and range as all real numbers.
  • Square Function
    A rule mapping each input to its square, producing a parabola opening upward with domain all real numbers and range from zero to infinity.
  • Cube Function
    A rule mapping each input to its cube, creating a curve symmetric about the origin with both domain and range as all real numbers.
  • Square Root Function
    A rule assigning each nonnegative input its principal square root, with domain and range both starting at zero and extending to infinity.
  • Cube Root Function
    A rule assigning each input its cube root, resulting in a curve passing through the origin with domain and range as all real numbers.
  • Slope-Intercept Form
    A linear equation format, y = mx + b, where m indicates steepness and b shows the y-axis crossing point.
  • Quadratic Function
    A degree-two polynomial, typically f(x) = ax² + bx + c, whose graph is a parabola with a vertex and axis of symmetry.
  • Vertex
    The highest or lowest point on a parabola, representing either a maximum or minimum value depending on the parabola's direction.
  • Axis of Symmetry
    A vertical line dividing a parabola into two mirror-image halves, always passing through the vertex.
  • Polynomial Function
    A rule involving only nonnegative integer exponents, always producing smooth, unbroken curves with domain all real numbers.
  • Degree
    The largest exponent in a polynomial, determining the function's overall shape and the number of possible turning points.
  • Rational Function
    A rule formed by dividing two polynomials, with domain restrictions wherever the denominator equals zero.
  • Exponential Function
    A rule with a constant positive base (not 1) raised to a variable exponent, producing rapid growth or decay.
  • Logarithmic Function
    A rule giving the power needed for a base to reach a number, serving as the inverse of an exponential function and featuring a vertical asymptote.