Unit 1 - AP Precalculus

Flashcards based on AP Precalculus exam prep reference sheet covering graphical behaviors, rates of change, polynomial and rational functions.

If the graph of f is increasing, what is the rate of change of f?

Positive

If the graph of f is concave up, what is the rate of change of f?

Increasing

If the graph of h is decreasing, what is the rate of change of h?

Negative

If the graph of g is concave down, what is the rate of change of g?

Decreasing

What are points of inflection?

Points where the graph of f changes from concave up to concave down (or vice versa)

What does the rate of change of f refer to?

The slope of the graph at a single point

Over equal-length input-value intervals, if the differences in the outputs are increasing, what type of function is it?

Concave up

Polynomial zeros always come in pairs.

Complex Zeros

If a factor is repeated n times, it has what?

Multiplicity

What does the leading term (highest degree) do?

Determines the end behavior of a polynomial function

What is the graphical symmetry of Even functions?

Graphs have symmetry over the y-axis

What is the graphical symmetry of Odd functions?

Graphs have symmetry over the origin

In Rational functions, how do you identify Holes?

Denominator equals 0 AND cancels out with numerator

In Rational functions, how do you identify Vertical Asymptotes?

Denominator equals 0 AND does NOT cancel out with numerator

In Rational functions, how do you identify Zeros?

Numerator equals 0

If degree of N is exactly 1 more than degree of D, the rational function has what?

Slant asymptote

What helps to quickly use the Binomial Theorem?

Pascal’s Triangle