– WE WANT TO FIND AN EQUATION FOR THE GRAPH OF THE DEGREE 5 POLYNOMIAL FUNCTION AND LEAVE THE FUNCTION IN FACTORED FORM. BECAUSE WE HAVE A DEGREE 5 POLYNOMIAL FUNCTION WE KNOW WE HAVE AT MOST FIVE REAL RATIONAL ZEROS OR ROOTS. SO LET’S ANALYZE OUR GRAPH. NOTICE THE GRAPH ONLY HAS TWO X…

# Tag: sousa

## Ex: Decompose Functions

– WELCOME TO THREE EXAMPLES OF EXPRESSING A FUNCTION AS A COMPOSITE FUNCTION. YOUR DIRECTIONS MAY ALSO SAY DECOMPOSE A GIVEN FUNCTION. HERE WE’RE GIVEN H OF X =THE QUANTITY 2X + 3 RAISED TO THE 3rd POWER. WE WANT TO WRITE H OF X AS A COMPOSITE FUNCTION IN THE FORM F OF G…

## Ex 7: Find the Zeros of a Degree 5 Polynomial Function

– WE WANT TO FIND ALL THE ZEROS OF THE FUNCTION GIVEN ONE OF THE ZEROS IS +3I. SO FIRST THING WE SHOULD RECOGNIZE HERE IS THAT WE HAVE A DEGREE FIVE POLYNOMIAL, SO WE SHOULD HAVE FIVE COMPLEX ZEROS. NEXT, WE’RE GIVEN ONE ZERO AS 3I, WHICH WE CAN THINK OF AS 0 +…

## Ex: Evaluate Composite Functions from Graphs

– WE WANT TO DETERMINE THE COMPOSITE FUNCTION VALUES FROM THE GRAPHS OF FUNCTION F IN BLUE AND FUNCTION G IN RED. FROM THIS DEFINITION HERE, WE SEE THERE ARE TWO WAYS TO EXPRESS A COMPOSITE FUNCTION. I THINK IT’S GOING TO BE HELPFUL TO REWRITE THESE COMPOSITE FUNCTIONS USING A NOTATION GIVEN HERE ON…

## Introduction to Functions of Two Variables

– WELCOME TO A VIDEO THAT WILL INTRODUCE FUNCTIONS OF TWO VARIABLES. THE GOALS OF THE VIDEO ARE TO DETERMINE FUNCTION VALUES OF FUNCTIONS OF TWO VARIABLES AND ALSO TO DETERMINE THE DOMAIN OF A FUNCTION OF TWO VARIABLES. THE FUNCTION Z=F OF XY IS A FUNCTION OF 2 VARIABLES. SO Z IS DEFINED IN…

## Evaluating Functions Using Function Notation (L9.3)

Welcome to a lesson on evaluating functions using function notation. An example of one we’re given that f of x equals x squared minus two x plus 11. So we’re given the formula for f of x, or the function rule. And because we have f of x here, we know that the input variable…

## Function Transformations: Horizontal and Vertical Stretches and Compressions

– WELCOME TO THE FIRST OF SEVERAL VIDEOS ON FUNCTION TRANSFORMATIONS. THIS VIDEO FOCUSES ON HORIZONTAL AND VERTICAL STRETCHES AND COMPRESSIONS. SO IF WE’RE COMPARING F(X) TO A FUNCTION IN THIS FORM, WE’LL BE LOOKING AT HOW THE VALUE OF “A” AND B AFFECT THE GRAPH OF THE ORIGINAL FUNCTION. SO IF WE HAVE Y=”A”…

## Ex: Probability of Events that are NOT Mutually Exclusive Events

– WELCOME TO TWO EXAMPLES OF DETERMINING PROBABILITY OF EVENTS THAT ARE NOT MUTUALLY EXCLUSIVE. IF IT IS POSSIBLE FOR TWO EVENTS TO OCCUR AT THE SAME TIME, THE EVENTS ARE NOT MUTUALLY EXCLUSIVE, SO IF EVENTS “A” AND B ARE NOT MUTUALLY EXCLUSIVE THEN THE PROBABILITY OF “A” OR B =THE PROBABILITY OF “A”…

## Ex: Find an Inverse Function From a Table

We want to find the inverse of a function, given here as a table. One way to think of an inverse function is a function that undoes. Or performs the opposite operation of the original function. So looking at function f. The x values are the inputs. And the y value are the outputs. So…