Mathematics Functions and Equations

Vocabulary flashcards covering polynomials, functions, rational equations, and key concepts in mathematics.

Polynomial Function

A sum of terms of coefficients and variables raised to a certain power, with exponents as nonnegative integers.

Average Rate of Change

Calculated using the formula (f(b) - f(a)) / (b - a), showing how much the function changes over the interval from a to b.

Zeroes of a Function

Values of x that make f(x)=0; can be found by setting the polynomial equation to zero.

Even Multiplicity

Occurs when a function touches the x-axis at a zero, indicating the function does not cross the axis.

Odd Multiplicity

Occurs when a function crosses the x-axis at a zero, indicating the function changes signs.

Power Function

A function of the form f(x) = k * x^n, where k is the constant of variation and n is the exponent.

Rational Function

A function that is the quotient of two polynomial functions, represented as a fraction.

Vertical Asymptotes

Lines where the function approaches infinity, occurring at x-values that make the denominator zero.

Horizontal Asymptotes

Lines that the graph of a function approaches as x approaches positive or negative infinity; determined by comparing degrees of numerator and denominator.

Slant Asymptote

Occurs when the degree of the numerator is one higher than that of the denominator; the asymptote can be found using polynomial long division.

X-intercepts

Points where the graph intersects the x-axis, found by solving f(x) = 0.

Y-intercepts

Points where the graph intersects the y-axis, found by evaluating f(0).

End Behavior

Describes the behavior of a function as x approaches positive or negative infinity.

Even Function

A function for which f(-x) = f(x), meaning it is symmetric about the y-axis.

Odd Function

A function for which f(-x) = -f(x), meaning it is symmetric about the origin.

Exponential Function

A function of the form f(x) = a * b^x, where a is the initial value and b is the growth factor.

Logarithmic Function

The function that converts exponentiation; y = log_b(x) corresponds to x = b^y.

Arithmetic Sequence

A sequence with a constant difference between consecutive terms.

Geometric Sequence

A sequence with a constant ratio between consecutive terms.

Law of Sines

A formula relating the sides and angles of non-right triangles: a sin(A) = b sin(B) = c sin(C).

Inverse Trig Functions

Functions that output angles instead of values, with restricted domains to ensure proper mapping.

Polar Function

A function that expresses points in terms of a radius (r) and an angle (θ) instead of Cartesian coordinates.

DeMoivre’s Theorem

A formula for raising a complex number in polar form to a power: z^n = r^n (cos(nθ) + isin(nθ)).