Chapter 1 Pre-Calc H

y=mx+b

slope-intercept form

y-y1=m(x-x1)

point slope form

Ax+By+C=0 where A>or equal to 0, A,B,C E Z, and A, B, C are relatively prime

standard/general form

the steeper the line

the bigger the absolute value....

a relation in which each element in the domain is paired with exactly one element in the range

function

numerically, graphically, algebraically, and verbally

what are the ways to represent a function?

table, mapping, ordered pairs

what are the ways to represent a function numerically?

name the function

what does f do in f(x)=x^2?

represents an element in domain

what does x do in f(x)=x^2?

represents the particular value in the range which f pairs with x

what does f(x) do in f(x)=x^2?

f(x+h)-f(x)/(x+h)-x

difference quotient

computes the slope of the secant through two points on a graph

what does the difference quotient do?

a function symmetric with respect to the y-axis

even function

a function symmetric with respect to the origin

odd function

a test used to determine if a relation is a function

vertical line test

the x-values for which f(x)=0

zeros of a function of f

a function f is increasing on an interval when all x, and x2 in the interval, x1

increasing function

a function f is decreasing on an interval when, all x, and x2 in the interval, x1f(x2)

decreasing function

|a|>1: vertical stretch by a factor of "a", 0

dilations in the range

|a|>1: horizontal compression by a factor of 1/a, 0

dilation in the domain

numbers, sets, and functions

what can you perform operations on?

addition and multiplication

what are the types of operations on numbers?

union, intersection, cartesian product

what are the types of operations on sets?

addition, multiplication, division, composition

what are the types of operations on functions?

the variation between two variables whose ratio is constant

direct variation

y/x=k, y=kx, y is proportional to x

direct variation equations

y=kx^n, n>0, y/x^n=k

equation for direct variation with a power on x

the variation between two variables whose product is constant

inverse variation

xy=k, y=k/x, y is proportional to 1/x

inverse variation equations

y=k/x^n, n>0, yx^n=k

equation for inverse variation with a power on x

one quantity varies directly with the product of two or moe other quantities

joint variation

multiple direct and inverse variations

combined variation