Show:
Reflections
Shifting
Dilation
Rules
Combined
100
-f(x)
Reflecting across the x axis
100
f(x+2)
Shifting left 2 units
100
2f(x)
Vertical Stretch
100
How do i know if I am reflecting?
If I see a negative in front or inside the function
100
-f(x+2) - 2
Reflecting across the x axis, shift 2 units left and 2 units down
200
f(-2x)
Reflecting across the y axis
200
f(x) + 2
Shifting 2 units up
200
1/2f(x)
Vertical Compression
200
Explain Vertical Stretching
When you multiply a number to the entire function
200
2f(x-2)+1
Vertical Stretch, shifting 2 units right and one unit up
300
-1/2f(x)
Reflecting across the x axis
300
f(x-3)
Shifting 3 units right
300
f(2/3x)
horizontal stretch
300
How is it different shifting left and right?
To shift left it is a function (x + 2) and to shift right is a function (x -2)
300
-2f(x+1)
Vertical Stretch, reflecting across the x axis, shifting one unit up
400
f(-2/3x)
Reflecting across the y axis
400
f(x) - 5
shifting 5 units down
400
f(2x)
horizontal compression
400
When you multiply the inside by a fraction, what is the transformation?
Horizontal Stretch
400
f(-2/3x +1)
reflecting across the y-axis, horizontal stretch, shifting one unit left
500
-2f(-2x)
Reflecting across the x and y axis
500
f(x-2) +1
Shifting 2 units right and one unit up
500
2f(1/2x)
Rarely ever seen, however the two transformations are vertical stretch and horizontal stretch
500
Name all the rules that you can with out your notes
4 rules, use note sheet
500
-2f(x+2)-4
Reflecting across x axis, vertical stretch, shifting left 2 units and 4 units down