– GIVEN F OF X =THE QUANTITY X + 2 SQUARED, WE WANT TO DETERMINE THE DOMAIN SO F OF X IS INCREASING AND 1 TO 1. WE ALSO WANT TO GIVE THE RANGE AND USE INTERVAL NOTATION. SO HERE’S A GRAPH OF OUR FUNCTION F OF X. NOTICE IF WE DON’T RESTRICT THE DOMAIN,…

# Tag: sousa

## Quadratic Functions – Find Vertex and Intercepts Using the Graphing Calculator

– IN THIS EXAMPLE, WE USE THE GRAPHING CALCULATOR TO FIND THE VERTEX, Y-INTERCEPT OR VERTICAL INTERCEPT, AND X-INTERCEPTS OR HORIZONTAL INTERCEPTS OF A QUADRATIC FUNCTION. IN THE PREVIOUS VIDEO, WE DID THIS BY HAND. SO, THE FIRST STEP IS TO ENTER THE FUNCTION INTO THE CALCULATOR. SO WE’LL PRESS Y EQUALS, CLEARING THE OLD…

## Ex: Find the Equation of a Quadratic Function from a Graph

– WE WANT TO DETERMINE THE EQUATION OF THE QUADRATIC FUNCTION FROM THE GRAPH. WE ALSO WANT TO GIVE THE FUNCTION IN GENERAL FORM. REMEMBER GENERAL FORM OF A QUADRATIC FUNCTION IS F OF X=AX/SQUARED + BX + C. BUT TO FIND THIS FORM OF THE FUNCTION, WE’RE ACTUALLY GOING TO USE THE STANDARD FORM…

## Introduction to Inverse Trigonometric Functions

– WELCOME TO AN INTRODUCTION TO INVERSE TRIGNOMETRIC FUNCTIONS. THE GOALS OF THE VIDEO ARE TO USE INVERSE TRIG FUNCTIONS TO FIND AN ANGLE OF A GIVEN TRIGNOMETRIC FUNCTION VALUE, AND ALSO TO USE INVERSE TRIGOMETRIC FUNCTIONS TO SOLVE A RIGHT TRIANGLE. REMEMBER, YOU CAN THINK OF A FUNCTION AND ITS INVERSE FUNCTION AS TWO…

## Ex 1: Key Characteristics of the Graph of a Quadratic Function (Opens Up)

– IN THIS PROBLEM WE’RE GIVEN THE GRAPH OF A QUADRATIC FUNCTION AND ASKED TO FIND ALL THE KEY CHARACTERISTICS. WE FIRST WANT TO START BY FINDING THE DOMAIN OF THE FUNCTION. REMEMBER THE DOMAIN IS A SET OF ALL POSSIBLE X VALUES OR INPUTS AND SINCE THE X AXIS IS THE HORIZONTAL AXIS HERE,…

## Function Transformations: Horizontal and Vertical Translations

– WELCOME TO ANOTHER VIDEO ON FUNCTION TRANSFORMATIONS. THIS VIDEO DEALS SPECIFICALLY WITH HORIZONTAL AND VERTICAL TRANSLATIONS, SO THE GOAL OF THE VIDEO IS TO GRAPH FUNCTIONS USING HORIZONTAL AND VERTICAL SHIFTS. IF WE ARE LOOKING AT TRANSFORMATIONS FROM THIS FUNCTION TO THIS FUNCTION, THIS VIDEO DEALS SPECIFICALLY WITH HOW C AND D TRANSFORM THE…

## Composite Functions

– 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…

## 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…