# Pre-Calculus – Quick Reference Sheet

Lines Relations and Functions
Increment: the change in coordinates
Slope: the change in vertical distance divided by the change in horizontal distance; frequently thought of as “Rise over Run”
Parallel Lines: two or more lines lines that never intersect; lines have the same slope
Perpendicular Lines: two lines that intersect at a angle. The product of their slopes will equal -1.
Formulas

 Equation of a line(Point-slope form) Equation of a line(General form) Equation of a line(slope-intercept form)
 Conic Sections

Definitions

Circle: the set of all points on a plane that are equidistant from the center.
Ellipse: the set of all points on a plane who distances from two fixed points in the plane have a constant sum.
Hyperbola: the set of all points on a plane who distances from two fixed points in the plane have a constant difference.
Parabola: the set of all points in a plane that are equidistant from a given fixed point and a given fixed line in the plane.
Semimajor axis, a: half the distance across an ellipse along the longest of the three principles axes.
Semiminor axis, b: half the distance across an ellipse along the shortest of the three principles axes.
Foci, F: the fixed point related to the construction and properties of a conic section.
Eccentricity, e: the distance from the center of the conic section to the focus point divided by the length of the semimajor axis

Definitions

Function: a rule that assigns exactly one element y in a set B (called the range) to each element x in a set A (called the domain)
Independent Variable: the number belonging to the set A
Dependent Variable: the number belonging to the set B
Vertical Line Test: If a vertical line intersects a curve at more than one point for any x, then the curve does not represent a function
the amount a function changes over a certain interval x
Vertical asymptote: the line x = a where the function f(x) approaches infinity as x approaches the value a
Horizontal asymptote: the line y = b where the function f(x) approaches the value b as x approaches infinity
Maximum: point on the curve where the function changes from increasing to decreasing
Minimum: point on the curve where the function changes from decreasing to increasing
Types of Functions

Algebraic Functions: a function where x is a constant; includes polynomial and rational functions
Polynomial Functions: a function in which x is raised to a power
Rational Functions: a function in which one polynomial is divided by a second (non-zero) polynomial
Absolute Value Functions: a function that takes the absolute value of a variable
Inverse Functions: a function where x and y are switched; noted as
Even Functions: a function is even if f(-x)=f(x)
Odd Functions: a function is odd if f(-x)=-f(x)
Parametric Equations: a set of equations where the functions x and y are dependant on a common variable t
One-To-One Functions: a function in which each value of the domain is mapped to only one value of the range
Parts of a Function

 Polynomial Function Rational Function Absolute Value Function Inverse Function if and only if Parametric Functions

Domain: the set of numbers for which x is defined
Range: the set of numbers for which y is defined
X-Intercept: the point where the function intersects the x-axis
Y-Intercept: the point where the function intersects the y-axis
Solution or Zero: the value of x where the function equals zero
Asymptote: a line that the function approaches but never touches
Points of Discontinuity: values of the function that are not defined

Transformation of Functions
Transformation on x: The curve will shift left or right along the x-axis by the amount of the transformation
Transformation on y: The curve will shift up or down along the y-axis by the amount of the transformation