Transformations change the size, shape, position, or orientation of a graph. Transformations are covered in the Chapter 1 of the Big Ideas Algebra 2 text and then again in the beginning of PreCalculus.
Remember: y = a(x-h)+k
Vertical Transformations
Changing something outside the parenthesis or absolute value lines moves the graph up and down.
Shift Down
Decrease k
Ex 1: y = x → y = x-1 (shift down 1)
Ex2: f(x) = 2(3x-5)+6 → g(x) = 2(3x-5)+4 (shift down 2)
Shift Up
Increase k
Ex 3: y = x → y = x+1(shift up 1)
Ex 4: f(x) = 2(3x-5)+6 → g(x) = 2(3x-5)+10 (shift up 4)
Vertical Stretch
Multiply outside ( ) or | | and k by a whole number.
Ex 5: y =|x| → y = 5|x| (vertical stretch by 5)
Ex 6: f(x)=2(3x-5)2+6 → f(x)=4(3x-5)2+12 (vertical stretch by 2)
Vertical Shrink
Multiply outside ( ) or | |and k by a fraction.
Ex7: y =|x| → y = 1/2|x| (vertical shrink by 1/2)
Ex8: f(x)=2(3x-5)2+6 → g(x) = 1(3x-5)2+3 (vertical shrink by ½)
Reflect Across X-Axis
Multiply outside ( ) or | |and k by a negative.
Ex9: y = x → y = -x (reflect across x-axis)
Ex10: f(x)=2(3x-5)2+6 → g(x)=-2(3x-5)2-6 (reflect across x-axis)
Horizontal Transformations
Changing something inside the parenthesis or absolute value lines moves the graph left and right.
Shift Left
Increase h
Ex11: y =|x| → y = |x+1| (shift left 1)
Ex12: f(x)=2(4x-6)2+8 → g(x) = 2(4x-4)2+8 (shift left 2)
Shift Right
Decrease h
Ex 13: y = |x| → y = |x-1| (shift right 1)
Ex 14: f(x)=2(4x-6)2+8 → g(x)=2(4x-10)2+8 (shift right 4)
Horizontal Stretch
Makes the graph fatter
Multiple inside ( ) or | |and h by a fraction.
Ex 15: y = |x| → y =|1/3x| (horizontal stretch by 3)
Ex 16: f(x)=2(4x-6)2+8 → g(x)=2(2x-3)2+8 (horizontal stretch by 2)
Horizontal Shrink
Makes the graph skinnier
Multiple inside ( ) or | |and h by a whole number.
Ex 17: y =|x| → y =|4x| (horizontal shrink by 1/4)
Ex 18: f(x)=2(4x-6)2+8 → g(x)=2(8x-12)2+8 (horizontal shrink by ½)
Reflect Across Y-Axis
Multiply inside ( ) or | |and h by a negative.
Ex 19: f(x)=2(4x-6)2+8 → g(x)=2(-4x+6)2+8 (reflect across y-axis)
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