transformations of functions - coach young math€¦ · transformations of functions...
TRANSCRIPT
![Page 1: Transformations of Functions - Coach Young Math€¦ · Transformations of Functions Transformations allow you to move a graph of a function into a new position w/out having to find](https://reader034.vdocuments.net/reader034/viewer/2022051814/6039e74c89592158a51f0011/html5/thumbnails/1.jpg)
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.
![Page 2: Transformations of Functions - Coach Young Math€¦ · Transformations of Functions Transformations allow you to move a graph of a function into a new position w/out having to find](https://reader034.vdocuments.net/reader034/viewer/2022051814/6039e74c89592158a51f0011/html5/thumbnails/2.jpg)
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
![Page 3: Transformations of Functions - Coach Young Math€¦ · Transformations of Functions Transformations allow you to move a graph of a function into a new position w/out having to find](https://reader034.vdocuments.net/reader034/viewer/2022051814/6039e74c89592158a51f0011/html5/thumbnails/3.jpg)
Describe the transformation(s):y = |x + 1|
Describe the transformation(s):y = √x + 2
![Page 4: Transformations of Functions - Coach Young Math€¦ · Transformations of Functions Transformations allow you to move a graph of a function into a new position w/out having to find](https://reader034.vdocuments.net/reader034/viewer/2022051814/6039e74c89592158a51f0011/html5/thumbnails/4.jpg)
Describe the transformation(s):y = 3(x + 4)2
Describe the transformation(s):y = |x 5| + 6
![Page 5: Transformations of Functions - Coach Young Math€¦ · Transformations of Functions Transformations allow you to move a graph of a function into a new position w/out having to find](https://reader034.vdocuments.net/reader034/viewer/2022051814/6039e74c89592158a51f0011/html5/thumbnails/5.jpg)
Describe the transformation(s):y = 4√x + 1
Describe the transformation(s):y = (x 7)2 1
![Page 6: Transformations of Functions - Coach Young Math€¦ · Transformations of Functions Transformations allow you to move a graph of a function into a new position w/out having to find](https://reader034.vdocuments.net/reader034/viewer/2022051814/6039e74c89592158a51f0011/html5/thumbnails/6.jpg)
Describe the transformation(s):y = 2(x + 3)2
Describe the transformation(s):y = 2|x + 3| 4
![Page 7: Transformations of Functions - Coach Young Math€¦ · Transformations of Functions Transformations allow you to move a graph of a function into a new position w/out having to find](https://reader034.vdocuments.net/reader034/viewer/2022051814/6039e74c89592158a51f0011/html5/thumbnails/7.jpg)
Describe the transformation(s):y = 3x3 + 2
Describe the transformation(s):y = |x| 81
4
![Page 8: Transformations of Functions - Coach Young Math€¦ · Transformations of Functions Transformations allow you to move a graph of a function into a new position w/out having to find](https://reader034.vdocuments.net/reader034/viewer/2022051814/6039e74c89592158a51f0011/html5/thumbnails/8.jpg)
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.
![Page 9: Transformations of Functions - Coach Young Math€¦ · Transformations of Functions Transformations allow you to move a graph of a function into a new position w/out having to find](https://reader034.vdocuments.net/reader034/viewer/2022051814/6039e74c89592158a51f0011/html5/thumbnails/9.jpg)
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.
![Page 10: Transformations of Functions - Coach Young Math€¦ · Transformations of Functions Transformations allow you to move a graph of a function into a new position w/out having to find](https://reader034.vdocuments.net/reader034/viewer/2022051814/6039e74c89592158a51f0011/html5/thumbnails/10.jpg)
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.
![Page 11: Transformations of Functions - Coach Young Math€¦ · Transformations of Functions Transformations allow you to move a graph of a function into a new position w/out having to find](https://reader034.vdocuments.net/reader034/viewer/2022051814/6039e74c89592158a51f0011/html5/thumbnails/11.jpg)
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.