IB Functions

Gradient-intercept form

The form of a linear equation written as y=mx+c, where m is the slope and c is the y-intercept.

Standard Form

The equation of a line written as ax+by=c.

Point-slope form

An equation of a line expressed as y-y1=m(x-x1), useful for finding the equation based on a slope and a point.

Parallel lines

Lines that have the same slope and do not intersect.

Perpendicular lines

Lines that intersect at a 90-degree angle.

Function

A relation that assigns exactly one output (y) for each input (x).

Domain

The set of possible input values (x) for a function.

Range

The set of possible output values (y) produced by a function.

Inverse function

A function that reverses the effect of the original function, switching x and y.

Self-inverse function

A function that is its own inverse, such that f(x)=f-1(x).

Even function

A function that satisfies f(-x)=f(x).

Odd function

A function that satisfies f(-x)=-f(x).

Absolute Maximum

The highest point on the graph of a function.

Absolute Minimum

The lowest point on the graph of a function.

Relative Maximum

A point on the graph where the value of the function is higher than at nearby points.

Relative Minimum

A point on the graph where the value of the function is lower than at nearby points.

Intercepts

Points where the graph crosses the axes; x-intercept where y=0, and y-intercept where x=0.

Vertical Asymptote

A line that a graph approaches but never touches, occurring where the denominator is zero.

Horizontal Asymptote

A value that a graph approaches as x tends towards positive or negative infinity.

Composite Function

A function created by plugging one function into another, denoted as (fg)(x)=f(g(x)).

Quadratics

Polynomial functions of degree 2, typically in the form ax^2 + bx + c.

Factorization

The process of breaking down a polynomial into its constituent factors.

Zero product property

If the product of two expressions equals zero, at least one of the expressions must equal zero.

Completing the square

A method for converting a quadratic function into vertex form by rearranging and adding terms.

Discriminant

A value calculated from the coefficients of a polynomial to determine the nature of its roots.

Rational functions

Functions that are expressed as the ratio of two polynomial functions.

Reciprocal functions

Functions of the form f(x)=1/x, characterized by having horizontal and vertical asymptotes at x=0 and y=0.

Exponential function

A function where the variable is in the exponent, typically in the form f(x)=a(b)^x.

Logarithmic function

The inverse of an exponential function, expressed in the form f(x)=a*log_b(x).

Transformations

Alterations to the graph of a function, including translations, stretches, and reflections.