Before we begin, I want to make sure you understand the importance of the 11 concepts listed below. The introduction of these concepts in this PREcalculus course is just that - an introduction. Becoming familiar with these concepts will help as you move through the AP Calculus course.
These concepts are the essence of calculus.
Limits - A limit in calculus describes the value that a function approaches as the input gets closer and closer to a specific value, without necessarily reaching it.
Continuity - The limits from the left and right exist and are equal to the value of the function at x = a.
Max and Min (extrema) Values - The largest (max) and smallest (min) values of a function.
Increasing and Decreasing functions -
Increasing: the values of y increase as x increases.
Decreasing: the values of y decrease as x increases.
Concavity (Concaves up/Concaves down) - Shape and direction of a curve.
Concaves up - opens up (upward facing cup - think of U)
Concaves down - opens down (upside down cup - think of ∩ )
Zeros - Where the graph crosses the x-axis and values that make the function equal to 0.
Multiplicities - The number of times the factor appears in a factored form of a polynomial. This is the exponent of the factor.
Points of Inflection - Points where the function changes concavity.
A point where concavity changes from up to down or down to up.
Asymptotes - Lines to which the graph of a function converges.
Vertical - a line where x = k (k is a constant)
Horizontal - a line where y = k
Degree of a function - The highest power of the variable in a polynomial.
End Behavior of a Function - The behavior of the graph of a function as x approaches positive/negative infinity.