– 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 +…

# Tag: james

## 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…

## Ex: Find the Linear Function Given Two Function Values in Function Notation

– HERE WE WANT TO DETERMINE THE EQUATION OF THE LINEAR FUNCTION GIVEN F OF -1=-7 AND F OF 2=-2. WHEN GIVEN FUNCTION VALUES IN FUNCTION NOTATION WE NEED TO RECOGNIZE THAT IF F OF -1=-7 THE INPUT OR THE X VALUE IS -1 AND THE OUTPUT OR THE FUNCTION VALUE OR Y WOULD BE…

## Graphing 9 Basic Functions

– WELCOME TO A QUICK REVIEW ON HOW TO GRAPH NINE BASIC FUNCTIONS. WE’LL BE GRAPHING THE NINE FUNCTIONS GIVEN HERE BELOW AND WITH PRACTICE WE SHOULD BE ABLE TO RECOGNIZE THE GRAPH AND THE EQUATIONS OF THESE NINE BASIC FUNCTIONS. NOW REMEMBER WHEN GRAPHING, IF WE’RE NOT SURE WHAT THE FUNCTION LOOKS LIKE WE…