What is a function?
One or more rules that assign certain inputs to exactly one output each
What is the domain of a function?
The set of all inputs that have a defined output in the function
What is the range of a function?
The set of all possible outputs of the function
What is a rational function?
A function [f(x)] that can be defined as [P(x)]/[Q(x)] where P(x) and Q(x) are polynomials
If P(x) has a higher degree than Q(x), is the rational function proper or improper?
Improper
If Q(x) has a higher degree than P(x), is the rational function proper or improper?
Proper
What is a root function?
A function [f(x)] defined as √(g(x)) where g(x) is a polynomial
What is a composite function?
A function where the output of one function is used as the input of the next [f(g(x))]
What is the domain of a composite function f(g(x))?
All numbers where x is an element of g’s domain and g(x) is an element of f’s domain [ x∈D(g) ∩ g(x)∈D(f) ]
What must f(x) satisfy to be an even function?
f(-x) = f(x)
What must f(x) satisfy to be an odd function?
f(-x) = -f(x)
What is a power function?
A function [f(x)] defined as a^x where a is a constant
What is an algebraic function?
A function constructed only from algebraic operations [+, -, *, /, √, etc.]
What is a piecewise function?
A function [f(x)] whose definition changes depending on the value of the input
What is a polynomial?
A function [f(x)] defined as a + bx + cx^2 + dx^3 + … where a, b, c, d, etc. are constants
When is a function [f(x)] increasing on the interval [a, b]? (a < b)
When f(a) < f(b)
When is a function [f(x)] decreasing on the interval [a, b]? (a < b)
When f(a) > f(b)
What are the six trigonometric functions?
sin(x), cos(x), tan(x), csc(x), sec(x), cot(x)
What is a tangent line?
A line that has the same instantaneous slope as a certain point on a curve, and touches that curve at that point.
What is a limit?
An estimation of a function’s output as its input gradually approaches some value from both sides
What is a one-sided limit?
An estimation of a function’s output as its input gradually approaches some value from one side
When is a limit defined for a function?
When the one-sided limits from both sides are equal, in which case the full limit is also equal
What is the first thing that should be done when solving a limit?
Substitute the terminating value into the function
If direct substitution in a limit results in an indeterminate form [ex. 0/0], what should be done next?
Simplify the function such that no indeterminate output exists, then substitute the terminating value again.
