Calculus

• a statement that two mathematical expressions are equal
• describes a relationship between two quantities

a set of numbers that can be substituted for the variables in an equation so that the equality is true

satisfy

a formula, rule or procedure for taking a set of numbers and assigning to each number x in the set precisely one value

• x in f(x); can be picked to be more or less any number
• an arbitrary number in the domain of a function f
• plays the role of a "placeholder"

f is a function of x

y = f(x) ; these values depend on those of x

defining y as a function of x

when an equation or function makes no sense at a particular point, it is said to be undefined at that point

the set of points where a function is defined

y; or the value of f at x

the set of all possible values of f(x) as x varies throughout the domain

• f(x) = mx + b
• m = slope
• b = y intercept

• f(x) = ax² + bx + c
• standard form = f(x) = a (x - h)² + k
• vertex = (h,k)
• a > 0 parabola opens upward; a < 0 opens downward