## International Mathematics Revision

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## Volume of rotation

Function Modeling and Volume of Rotation

Modeling Flower Vase

Objective:

• Identify the mathematical model function fits the outline of the vase
• Volume of Rotation
• Hybrid functions modeling

Question no : 1

## Counting Principles

Vertical line test is a visual way of determining that the given relation is a function or not. If the vertical line drawn intersects the graph of the relation at more than one point then the given relation is not a function. If it intersect at one point then it is a function. With the vertical line test we check the one to one relation. A function can have only one y value for each unique value of ‘x’.

Subtraction of two Vectors

Vertical line test is a visual way of determining that the given relation is a function or not. If the vertical line drawn intersects the graph of the relation at more than one point then the given relation is not a function. If it intersect at one point then it is a function. With the vertical line test we check the one to one relation. A function can have only one y value for each unique value of ‘x’.

## Direction Cosines

Vertical line test is a visual way of determining that the given relation is a function or not. If the vertical line drawn intersects the graph of the relation at more than one point then the given relation is not a function. If it intersect at one point then it is a function. With the vertical line test we check the one to one relation. A function can have only one y value for each unique value of ‘x’.

Subtraction of two Vectors

Vertical line test is a visual way of determining that the given relation is a function or not. If the vertical line drawn intersects the graph of the relation at more than one point then the given relation is not a function. If it intersect at one point then it is a function. With the vertical line test we check the one to one relation. A function can have only one y value for each unique value of ‘x’.

Subtraction of two Vectors

## Scalar multiplication of a vector

Scalar multiplication of a Vector

Vertical line test is a visual way of determining that the given relation is a function or not. If the vertical line drawn intersects the graph of the relation at more than one point then the given relation is not a function. If it intersect at one point then it is a function. With the vertical line test we check the one to one relation. A function can have only one y value for each unique value of ‘x’.

## Unit vectors

1. Vertical line test

Vertical line test is a visual way of determining that the given relation is a function or not. If the vertical line drawn intersects the graph of the relation at more than one point then the given relation is not a function. If it intersect at one point then it is a function. With the vertical line test we check the one to one relation. A function can have only one y value for each unique value of ‘x’.

3. Interactive Graph

Use the interactive graph given below to draw the graph of any relations. Use the input box to enter any relation and  use the start and reset buttons to animate the vertical line and using vertical line test determine that the relation is a function or not.

## Three dimensional vectors

1. Vertical line test

Vertical line test is a visual way of determining that the given relation is a function or not. If the vertical line drawn intersects the graph of the relation at more than one point then the given relation is not a function. If it intersect at one point then it is a function. With the vertical line test we check the one to one relation. A function can have only one y value for each unique value of ‘x’.

3. Interactive Graph

Use the interactive graph given below to draw the graph of any relations. Use the input box to enter any relation and  use the start and reset buttons to animate the vertical line and using vertical line test determine that the relation is a function or not.

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