transformations of functions - coach young math€¦ · transformations of functions...
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Transformations of FunctionsTransformations allow you to move a graph of a function into a new position w/out having to find new ordered pairs to plot on the graph.
Parent Function most simple form of function
Absolute Value: y = |x| Quadratic: y = x2
Square Root: y = x Cubic: y = x3
Parent Functions with Transformation Options
***Knowing these will help you out***
Quadratic y = x2 y = a(x h)2 + k
Absolute Value y = |x| y = a|x h| + k
Square Root y = x y = a√x h + k
Cubic y = x3 y = a(x h)3 + k*They all have the same location of the a, h, and k.
Transformations of Functions
y = f(x) + k shifts f(x) up k unitsy = f(x) k shifts f(x) down k unitsy = f(x h) shifts f(x) right h unitsy = f(x + h) shifts f(x) left h unitsy = f(x) reflects f(x) over xaxisy = a(f(x)), a > 1 vertically stretches f(x) y = a(f(x)), 0<a<1 vertically compresses f(x)
Transformations by a/h/k value:
reflected over xaxis avertically stretched a > 1vertically compressed 0 < a < 1
shift left + hshift right h
shift up + kshift down k
a
h
k
Describe the transformation(s):y = |x + 1|
Describe the transformation(s):y = √x + 2
Describe the transformation(s):y = 3(x + 4)2
Describe the transformation(s):y = |x 5| + 6
Describe the transformation(s):y = 4√x + 1
Describe the transformation(s):y = (x 7)2 1
Describe the transformation(s):y = 2(x + 3)2
Describe the transformation(s):y = 2|x + 3| 4
Describe the transformation(s):y = 3x3 + 2
Describe the transformation(s):y = |x| 81
4
Remember:
Quadratic y = a (x h)2 + k
Absolute Value y = a | x h | + k
Square Root y = a √ x h + k
Cubic y = a (x h)3 + k
Write the function given the transformations.
Square root function that is reflected over the xaxis and shifted right 3 units.
Write the function given the transformations.
Quadratic function that is vertically stretchedby a factor of 4 and shifted down 2 units.
Write the function given the transformations.
Cubic function that is reflected over the xaxis, shifted down 5 units, and shifted right 3 units.
Write the function given the transformations.
Absolute value function that is reflected over the xaxis, vertically compressed by a factor of .25, shifted down 2 units, and shifted left 3 units.
The graphed blue function is the parent function. Describe the transformation(s) from the parent function (blue) to the
function given (green). Write the equation of the green graph.
The graphed blue function is the parent function. Describe the transformation(s) from the parent function (blue) to the
function given (green). Write the equation of the green graph.