3.7 Operations on Functions 10/18/11

In this section, we looked at defining functions using various operations and combining multiple expressions using new methods.

First, we will take a look at the basic operations of functions: sum, difference, product, and quotient.

Sum:

---->  


Difference:

  ---->  


Caution: Remember to distribute the negative when inserting the g(x) expression.

Product:


  ---->


Quotient:


    ---->  



A sample of the sum method:




Find
Since this^^ = 
Then:






Next, we began to look into compositie functions.

The composite function  f  ° g  of two functions f  and g is defined by:

(f  ° g)(x) = f(g(x))


The domain of  f  ° g is the set of all x in the domain g such that g(x) is in the domain of f.

An example of a composite function problem:

Let  and 

(f  ° g)(x) 

(f  ° g)(x)

(f  ° g)(x)

(f  ° g)(x)

Domain problems are also common in this section, so be ready to find the domain of functions like we did in previous chapters.

Hope this helped!

-julia

3.6: Quadratic FUNctions

QUADRATIC FUNCTIONS are those funky-looking curved graphs with equations that have multiple xs and confusing exponents in them.

A function f is a QUADRATIC FUNCTION if and only if it fits in the form where a, b, and c are real numbers with a not equal to zero.

What can you figure out from a QUADRATIC FUNCTION?

a: if positive, the funtion opens up; negative, the funtion opens down

it controls the width of the graph

b: controls how the vertex moves along the inversion of the function

c: the y intercept

VERTEX: The minimum or maximum value of the function (minimum if a>0; maximum if a<0)

The coordinate of the vertex of a parabola is

AXIS OF SYMMETRY: That dotted line down the middle of the parabola that runs through the VERTEX.

on the right is the STANDARD FUNCTION

of a parabola with Vertex V(h,k)

You can make your ugly QUADRATIC EQUATION into a fashionable STANDARD EQUATION by simply completing the square, as demonstrated on the right.