The number that a variable is multiplied by. For example, in the expression, `3x`, the coefficient of `x` is `3`. Every variable has a coefficient. If the coefficient is `1`, it is not written explicitly, but the variable in the term `x` has an assumed coefficient of `1`.
Having degree 3; a 3rd order term; a variable with an exponent of 3. A cubic equation is represented by a curve with at most 2 changes of direction (the degree - 1 = 2).
A math sentence containing an `=` sign. The expressions on the left side of the `=` sign have the same value as the expressions on the right side.
A number that is written to the right and slightly above another number or variable (the base number) that indicates how many times to multiply the base number by itself. It is a shorthand for multiplying a number by itself many times. For example, `3^2` means to multiply `3` by itself `2` times and is equal to `3 times 3 = 9`; `5^3` is equal to `5 times 5 times 5 = 125`; and `y^2` is equal to `y times y`.
There are single-variable functions and multi-variable functions. Prior to Calculus, almost all functions are single-variable. A single-variable function is a 1-to-1 relationship between two variables. One of the variables is the independent variable, and the other variable is the dependent variable. It is standard practice in mathematics to use the letter `x` to represent the independent variable and `y` to represent the dependent variable. Thus each value of `x` will determine the value of `y`; the function is what maps the `x` value to the `y` value. In a 1-to-1 relationship (a function) each value of `x` gets mapped to exactly one value of `y`.
Shorthand for 'if and only if'. This is short-hand for a logic statement that combines an if-then logic statement with its converse statement indicating that they are both true, or they are both false. Given the statement, 'if `p`, then `q`,' its converse statement is 'if `q`, then `p`.' The statement '`p` iff `q`' means that both 'if `p`, then `q`' and 'if `q`, then `p`' are either true or both are false.
Something is inversely proportional to another thing if they move in opposite direction. So `y` is said to be inversely proportional to `x` if when `x` increases, `y` decreases; and when `x` decreases, `y` increases. Two variables that are inversely proportional are related by the equation: `y=k/x` where `k` is a constant.
Having degree 1; a 1st order term; a variable with an exponent of 1. A linear equation is represented by a line. Its graph has 0 changes of direction (the degree - 1 = 0).
Something is proportional or also said to be directly proportional to another thing if they move in the same direction. So `y` is said to be proportional to `x` if when `x` increases, `y` also increases; and when `x` decreases, `y` also decreases. Two variables that are directly proportional are related by the equation: `y=kx` where `k` is a constant.
Having degree 2; a 2nd order term; a variable with an exponent of 2. A quadratic equation is represented by a parabola or a hyperbola. Its graph has 1 change of direction (the degree - 1 = 1). Note: Although ‘quad’ usually refers to the number 4, in this case it does not. Instead ‘quadratic’ derives from the Latin word ‘quadratum’ which means square. Thus, a quadratic is square-like referring to a 2nd order term or equation.
A measure of the steepness of a line. It is calculated by dividing the resulting change in the value of the `y` coordinate by a change in the value of the `x` coordinate.
A letter that is used to represent a range of possible values where the value varies depending on different factors. A variable just represents a number; anything that can be done to numbers can be done to variables also.