Transformation

Hey kidz!!! I am here to summarize and explain in english what we learned so far.

Vocabularies : 

Transformation - moving the function to a different position keeping its original size, area and line length.

Translation-moving the function in a different position without rotating or flipping.
Reflection- A transformation in which a geometric function is reflected across a line, creating a mirror image. 

I will tell you how the equation affects the function by showing this formula:

y= Af(B (x+C))+D 

A affects the "y -coordinate". Multiply the "y value" to the value of A.(whatever the value is,use it)

D affects the "y-coordinate". Add or subtract the "y value" to the value of D.(whatever the value is, use it)

B affects the "x-coordinate". Multiply the "x value" to the reciprocal of B.(whatever the value is, get its reciprocal and use it)

C affects the "x-coordinate". add or subtract. the "x value" to the reciprocal of C.(if the value is positive, add or subtract it with its negative value. vice versa )

-for Y multiply "A" first then add/subtract D.(if both are given)

-for X multiply B first then add/subtract C.(remember if C is positive, make it negative. if C is negative make it positive.)(if both are given)

Now I will show you how each of them affects the function by giving examples:

1) y=f(x-2)

 definition:function f(x) was horizontally translated 2 units to the right.

 English: the whole function was moved 2 units to the right.

  

2)y=f(x+2)

 definition: function f(x) was horizontally translated 2 units to the left.

 English the whole function was moved 2 units to the left.

NB: if it's f(x-y), the graph will move to the right. if it's f(x+y), the graph will move to the right. opposite right? Deal with it.

3)y=f(x)-2

definition: function f(x) was vertically translated 2 units down.

English: the whole function was moved 2 units down.

4)y=f(x)+2

definition: function f(x) was vertically translated 2 units up.

english: the whole function was moved 2 units up.

5) y=1/2 f(x)
definition: the function f(x) was vertically stretched by a factor of 1/2 about the x-axis.
English: the whole f(x) will open wider.


6) y=2f(x) 
definition: the function f(x)  was vertically stretched by a factor of 2 about the x-axis.
English:the whole function will open narrower.


7) y= f(2x) 
definition: the function f(x) was horizontally stretched by a factor of 2 about the x-axis.
English:the whole function will open narrower.

8) y= f(1/2x)
definition: the function f(x) was horizontally stretched by a factor of 1/2 about the x-axis.
English:the whole function will open wider.



I hope I explained it to you very well in terms we can all understand. GG