Function Transformation Lesson
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
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) = x2 + 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)= x2 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