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1. Consider the function 𝑓(𝑥) = −√𝑥 + 2   + 3.

 Sketch the parent function here and then fully explain ALL of the transformations required to produce this function from the parent function.

 

Graph the function (2 points) 𝑓(𝑥) = −√𝑥 + 2   + 3 ( the square root sign goes over x+2 but NOT 3) 

 

 State the domain and range of the function above

 Mar 18, 2022
 #1
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The parent function is:  y  =  sqrt(x)

To get  y  =  sqrt(x + 2)  translate the function two units to the left (horizontally).

To get  y  =  -srt(x + 2)  flip the function over the x-axis.

To get  y  =  -sqrt(x + 2) + 3  translate the function 3 units up (vertically).

 

Domain:  x >= -2

Range:  y <= 3

 Mar 18, 2022

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