4.) Sketch the graph of each function using transformations of the function's characteristic features and a minimum number of plotted points. Clearly state in words what transformations are applied. Be sure to identify/label all vertices and x & y-intercepts as applicable. f (x) = -|x – 2| + 3 q(x) = V-(x + 3) – 1 %3D

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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4.) Sketch the graph of each function using transformations of the function's characteristic features and
a minimum number of plotted points. Clearly state in words what transformations are applied. Be
sure to identify/label all vertices and x & y-intercepts as applicable.
f (x) = -|x – 2| + 3
q(x) = V-(x + 3) – 1
%3D
Transcribed Image Text:4.) Sketch the graph of each function using transformations of the function's characteristic features and a minimum number of plotted points. Clearly state in words what transformations are applied. Be sure to identify/label all vertices and x & y-intercepts as applicable. f (x) = -|x – 2| + 3 q(x) = V-(x + 3) – 1 %3D
Expert Solution
Step 1

 

Part (a) :Here the original function is  fx=x

Horizontal translation:

 

Now the parameter 2 subtracted from the input x, the function become fx-2=x-2

 

Vertically Reflection:

 

Unit -1 is multiplied by the function x-2, so the function fx-2 is vertically reflected over the x-axis.

 

Vertical translation:

 

Unit 3 is added to the output of the function -x-2, then the function become -x-2+3

 

 

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