# Function Transformation Lesson

- Author:
- Satvinder Singh

## Discover the Stretch, Compression ,Horizontal and Vertical shifts

## You may try to Change the numbers which cause different effects of the functions

First Enter your main Function and then change the values to see the transformed function

## Notes-1

Use the Applet above and check this:
We can stretch or compress f(x) in the y-direction by multiplying the whole function by a constant.
if C> 1 : it will stretch the f(x) in the y-direction
if 0 < C < 1: it will compress the function in the y-direction.
go up and try

## Notes-2

Use the Applet above and check this:
We can stretch or compress f(x) in the x-direction by multiplying 'x' by a constant.

- D > 1 compresses it
- 0 < D < 1 stretches it

**bigger**values cause more**compression**.## Using Notes 1 & 2 answer the following questions

Q1. Compare g(x) with f(x)

## Q2.

Compare g(x) with f(x)

## Q3.

Compare g(x) with f(x)

## Notes-3

We can move it

**up or down by adding a constant**to the y-value g(x) = x^{2}+ K or Note: to move the line**down**, we use a**negative**value for K.- K > 0
**moves it up** - K < 0
**moves it down**

## Notes-4

We can move it

**left or right by adding a constant**to the x-value g(x) = (x+h)^{2}or Note:**Adding h**moves the function to the**left**(the negative direction).- h > 0
**moves it left** - h < 0
**moves it right**

## Based on Notes 3 and 4 answer these Questions

Q4. if and compare g(x) with f(x)

## Q5.

if and compare g(x) with f(x)

## Q6. Use all the facts you have learned

if and compare g(x) with f(x)

## Q7. What would be g(x) if

we transform f(x)= x^{2
}such that it **compresses by a factor of 3 in the x-direction** , shift the function by **2 on the left of y-axis** and **move 4 units to Up**