General Mathematics Reviewer

Rational Function

is a function of the form f(x) p(x)/q(x) where p(x) and q(x) are polynomials and q(x) ≠ 0

Asymptote

a line that a curve approaches but does not intersect

Vertical Asymptote

a vertical line of the form x = a which the curve approaches but never touches ; the vertical line passing through the zeroes of the denominator of the rational functions

Horizontal Asymptote

a horizontal line of the form y = b which the curve approaches but never touches

Rational Expression

is a fraction whose numerator and denominator are both polynomials

Rational Equation

is an equation whos terms are rational expressions

Least Common Denominator

is the common multiple of the denominators

Solutions

or roots, are values that satisfy a given rational equation

Extraneous Solution

values that arrived upon solving a rational equation but do not satisfy the given equation

Domain of a Function

the set of all values of x that have corresponding values of y ; it contains all values that go into the function

Range of a Function

the set of all values of y that can be obtained from the possible values of x ; it contains all possible values of the function

Holes

if there’s a common factor in numerator and denominator

Exponential Functions

a function in the form f(x)=ka^x where 𝑎>0, 𝑎≠1, 𝑘≠0, and 𝑥 is any real number

Exponential Growth

an exponential function of the form f(x)=ka^x where 𝑎>1 and 𝑘>0; the value of 𝑓(𝑥) increases without bound

Exponential Decay

an exponential function of the form f(x)=ka^x where 0<𝑎<1 and 𝑘>0; the value of 𝑓(𝑥) decreases

Half-life

the time it takes for half of a radioactive substance to decay

Compound Interest

refers to the sum of interests of prior periods computed on the original or principal amount and each of the successive periods on both the principal and the interest

Vertical Shift

occurs when a constant is added to a given exponential function, causing its entire graph to move upward or downward on the Cartesian plane

Horizontal shift

occurs when a constant is added to the exponent of a given exponential function, causing its entire graph to move to the left or to the right

Exponential Equations

equations that involve a variable as an exponent

Inverse Functions

a function g is the inverse function of f if the ordered pairs of g are are the ordered pairs of f written in reversed order

One-to-one Function

a function is one-to-one if every second element is paired to only one first element ; moreover, a function has an inverse function if and only if it is one-to-one

Horizontal Line Test

if any horizontal line drawn anywhere on the graph intersects the graph exactly once, then the graph is one-to-one

Logarithmic Function

it is a function which follows the form f(x)=logb x, where 𝑥>0, 𝑏>0. and b≠1; it is the inverse of the exponential function

Common Logarithm

logarithm with a base of 10; written as log⁡ 𝑥

Natural Logarithim

logarithm with a base of 𝒆 (Euler’s number); written as ln⁡ x