Translation of Lines Function

M4L19: Translating Graphs of Functions

You will need your graphing calculators today.​

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Transformations of

Linear Functions 

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the parent function is y = x    

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​Use your graphing calculator to graph part a from Opening Exercises on page 111:

f(x) = x

g(x) = x + 5

h(x) = ​x - 6

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• How are these graphs the same?

• How are they different?

• Can you find the x and y intercepts for each ?

• What type of transformation did they all undergo?

How are these graphs similar? Different?​

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Transformations of

Quadratic Functions 

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the parent function is y = x²

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• How are these graphs the same?

• How are they different?

• What is the vertex for each?

• What type of transformation did they all undergo?

​Pg. 111: Opening Exercise (part b)

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Transformations of

Absolute Value Functions 

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the parent function is

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• How are these graphs the same?

• How are they different?

• What is the vertex for each?

• What type of transformation did they all undergo?

​Pg. 111: Opening Exercise (part c)

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Test your transformation skills...

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Multiple Choice

Which formula best matches the translated graph from the parent function?

• $$f\left(x\right)=x^2+4$$

• $$f\left(x\right)=\left(x+4\right)^2$$

• $$f\left(x\right)=\left(x-4\right)^2$$

• $$f\left(x\right)=x^2-4$$

Multiple Choice

Which formula best matches the translated graph from the parent function (purple to black)?

• $$f\left(x\right)=\sqrt{x}+5$$

• $$f\left(x\right)=\sqrt{x+5}$$

• $$f\left(x\right)=\sqrt{x-5}$$

• $$f\left(x\right)=\sqrt{x}-5$$

Multiple Choice

Which formula best matches the translated graph from the parent function (red to blue)?

• $$f\left(x\right)=\left|x-2\right|-3$$

• $$f\left(x\right)=\left|x+2\right|-3$$

• $$f\left(x\right)=\left|x+2\right|+3$$  

Multiple Choice

Which graph best matches the function $$f\left(x\right)=-\left(x+1\right)^2+3$$  

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