ap-precal midterm

input-output

input values = independent values = domain = x
output values = dependent values = range = y

average rate of change

the ratio of the change in output values to the change in the input values over an interval

concave up

the average of change over equal-length input value intervals is increasing for all small-length intervals

concave down

the average of change over equal length input value intervals is decreasing for all small length intervals

polynomial functions

"poly" means many of much. A nonconstant polynomial is a function with many terms

increasing

the function is rising as we move from left to right

decreasing

the function is falling as we move from left to right

change in rate of change

the change in the ratio of the change in output values to the change in the input values over an interval

secant line

a line connecting two points (a,b) used to find the rate of change

point of inflection

occurs when a function changes from concave up to concave down to concave up

degree

the largest exponent of a polynomial function

leading coefficient

the numbers written in front of the variable with the largest exponent (a*n)

even/odd

an even function is symmetric over the y-axis
an odd function is symmetric about the origin

end behavior

the "left" and "right" side of a polynomial function graph will go "up" or "down"

limit left
limit right

x values are -> negative infinity
x-values are -> positive infinity

conjugate

all imaginary roots come in pairs. if a + bi is a root of f(x), then so is a-bi. conjugate pairs

multiplicity

the multiplicity of a zero is the degree of its factor

tangent

the graph bounces off the x-axis

transformation

vertical translation, horizontal translation, vertical dilation, horizontal dilation

dilations

nonrigid transformation enlarge or compress the graph vertically or horizontally stretch or shrinks

translations

ridgid movement, horizontally or vertically

local/relative extrema

(maxima and minima)
increasing to decreasing = local, relative, maxima output value
decreasing to increasing = local, relative, minima output value

global/absolute extrema

of all local maxima, the greatest
of all local minima, the least

rational functions

the ratio of two polynomials where the polynomial in the denominator cannot equal 0

horizontal asymptotes

the line y=b is a horizontal asymptote of the graph of f when lim f(x) = b or lim f(x) = b
x-> -∞ x-> ∞

vertical asymptotes

occurs when a factor in the denominator cannot cancel out with factors in the numerator

slant asymptotes

if the degree of the numerator is exactly 1 greater than the degree of the numerator

holes

occurs when the factor in the denominator cancels out with the factors in the numerator

polynomial long division

used to rewrite a rational function r(x)= f(x)/g(x) into the form f(x) = q(x) • g(x) + r(x) where q(x) is the quotient and r(x) is the remainder

limit notation

used to describe the behavior of a function as the input values approach a certain value
lim f(x) = lim f(x) =
x-> -∞ x-> ∞

regression

use a table of data to complete a regression on your calculator to model a function

pascals triangle

use a row in pascals traingle use a row in pascal's triangle to expand a function in the form of p(x) = (x + c)^n

zeros : real and non-real

the graph intersects the x-axis when the output value is 0. the corresponding input values are said to be zeros of the function. non-real zero is imaginary