Function Transformation Applet

Discover the Stretch, Compression 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
Note that (unlike for the y-direction), bigger values cause more compression.

Using Notes 1 & 2 answer the following questions

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

Check all that apply

Q2.

Compare g(x) with f(x)

Check all that apply

Q3.

Compare g(x) with f(x)

Check all that apply

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
will move 3 units to the right of the y-axis , beause x-3= 0 or x= 3 (positive menas right) will move 4 units to the left of y-axis because x+4= 0 means x= -4 ( so left)

Based on Notes 3 and 4 answer these Questions

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

Check all that apply

Q5.

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

Check all that apply

Q6. Use all the facts you have learned

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

Check all that apply

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