functions

A function is one to one when each x-value corresponds to only one y-value and each y-value corresponds to just one x-value.

One-to-One Functions

One-to-one functions come up in section 11.1. A one-to-one function is a function where each x-value corresponds to only one y-value, and each y-value corresponds to only one x-value.

An example of this is:

a. (1,2), (3,8), (9,0)

This IS a one-to-one function because each x and y-value only appears once throughout the ordered pairs.

b. (4,7), (8,6), (4,3)

This IS NOT a one-to-one function because the 4 shows up throughout the ordered pairs twice as the x-value.

Helpful website for conic sections

http://www.intmath.com/plane-analytic-geometry/conic-sections-summary.php
General Form of the Circle

An equation which can be written in the following form (with constants D, E, F) represents a circle:

x2 + y2 + Dx + Ey + F = 0
Formal Definition A circle is the locus of points that are equidistant from a fixed point (the center).
Conic Section



If we slice one of the cones with a plane at right angles to the axis of the cone, the shape formed is a circle.

While doing the HW problems today I forgot that terms like (x+5)^2 are written as (x+5)(x+5) - I was writing the problem as x^2+25. This is a small but critical error that could make all the difference on the up coming test.
That's all...Weeeeerd Up!

Composition Functions

When you apply a function rule to the result of another function rule you compose a function.

-you MUST know the notation to compose.

Notation: f(g)(x)= f(g(x))
pronounce- “f of g of x”
f composed of g composed of x.

-all functions are composed of x, x is the input.

f(g(x)) is the same as (fog)(x)

f(x)= x^2+4 g(x)= 2x+3

now instead of putting x as the input, put g(x).
f(g(x))=(2x+3) then apply all of the x values from the x problem
f(g(x))= (2x+3)^2+4
simplify
=(2x+3)(2x+3)+4
=4x^2+6x+9+4
f(g(x))= 4x^2+12x+13

Ex1: Find (gof)(2)
=g(f(2))
1. Always work inside out by plugging the input values in.
=g(f(2))= g(8)

12.1 functions

f(x)=x^2- the squaring function

f(x)=|x|- absolute value function

f(x)=1/x the reciprocal function

f(x)=√ x square root function

12.1 exercises HW

for problems 5-18 you can put the function in your caculator and see what the graph is supposed to look like. It really helps