– WELCOME TO A VIDEO ON COMPOSITE FUNCTIONS. A COMPOSITE FUNCTION CAN BE THOUGHT OF AS A COMBINATION OF TWO FUNCTIONS. ONE WAY TO ILLUSTRATE THIS WOULD BE TO USE A CONVEYOR BELT WHERE WE HAVE AN INITIAL INPUT OF, LET’S SAY, 3, ONE WAY TO ILLUSTRATE THIS WOULD BE TO USE A CONVEYOR BELT…

# Tag: sousa

## Ex: Determine if a Table of Values Represents a Function

– WE WANT TO DETERMINE WHICH OF THE FOLLOWING TABLES REPRESENT FUNCTIONS. A FUNCTION IS RELATION IN WHICH EVERY INPUT HAS EXACTLY ONE OUTPUT. SO LOOKING AT THESE TABLES, THE X VALUES WILL BE THE INPUTS AND THE Y VALUES WILL BE THE OUTPUTS. SO IF THESE TABLES ARE FUNCTIONS, WE COULD SAY THAT EVERY…

## Finding Function Values

– FIND FUNCTION VALUES. OUR GOAL IS TO EVALUATE A GIVEN FUNCTION GIVEN DIFFERENT INPUTS. I’D LIKE TO RELATE THIS TO SOME THAT WE’VE ALREADY DONE THIS SEMESTER. MANY TIMES FUNCTIONS ARE WRITTEN UP AS EQUATIONS LIKE Y=5X – 2 OR Y=X SQUARED + 4. BEFORE WHEN WE WERE FIND POINTS ON THE GRAPHS OF…

## Ex: Determine the Velocity Function and Acceleration Function from the Position Function

– THE FOLLOWING FUNCTION GIVES THE HEIGHT OF A PROJECTILE IN METERS AFTER T SECONDS. WE WANT TO DETERMINE THE HEIGHT, VELOCITY, AND ACCELERATION AFTER THREE SECONDS. BEFORE WE DO THIS, LETS TAKE A LOOK AT THE GRAPH OF THIS FUNCTION. WE’VE ALREADY TYPED IN THE FUNCTION INTO Y1 AND I’VE ALREADY ADJUSTED THE WINDOW…

## Differentials of Functions of Two Variables

– WELCOME TO A LESSON ON DIFFERENTIALS FOR FUNCTIONS OF TWO VARIABLES. IN CALCULUS ONE WE LEARNED THAT FOR FUNCTIONS OF ONE VARIABLES DIFFERENTIAL Y OR DY WAS EQUAL TO F PRIME OF X x DX. WELL, FOR FUNCTIONS OF TWO VARIABLES, MEANING Z IS DEFINED IN TERMS OF X AND Y, X AND Y…

## Introduction to Hyperbolic Functions

– WELCOME TO AN INTRO TO HYPERBOLIC FUNCTIONS. IN THIS VIDEO WE’LL DEFINE THE HYPERBOLIC FUNCTIONS, GRAPH THE HYPERBOLIC FUNCTIONS AND ALSO STATE THE PROPERTIES OF HYPERBOLIC FUNCTIONS. HYPERBOLIC FUNCTIONS ARE EXPONENTIAL FUNCTIONS BUT THEY SHARE SIMILAR PROPERTIES TO TRIGONOMETRIC FUNCTIONS. RIGHT AWAY NOTICE HOW THERE ARE SIX HYPERBOLIC FUNCTIONS AND THERE ARE ALSO SIX…

## Functions Transformations: A Summary

– WELCOME TO A SUMMARY OF FUNCTION TRANSFORMATIONS. THIS VIDEO WILL REVIEW HOW THE VALUES OF “A,” B, C AND D TRANSFORM THE FUNCTION OF F OF X. LET’S FIRST TALK ABOUT THE VALUE OF “A.” Y=”A” x F OF X. FOR “A” GREATER THAN 1, WE’LL STRETCH THE GRAPH OF F OF X VERTICALLY…

## Ex: Sketch the Graph of a Derivative Function Given the Graph of a Function

– WE WANT TO GRAPH THE FUNCTION THAT WOULD GIVE THE SLOPE WITH THE TANGENT LINES TO THE GIVEN FUNCTION GRAPHED HERE IN RED. WELL, THE FUNCTION THAT GIVES THE SLOPE WITH THE TANGENT LINES WOULD BE THE DERIVATIVE FUNCTION. SO WE’RE GIVEN F OF X. WE WANT TO GRAPH F PRIME OF X. SO…

## Ex2: Find an Equation of a Degree 5 Polynomial Function From the Graph of the Function

– 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…