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The region between the graph of y=f(x) and the x-axis, shaded in this figure, has an area of 10 square units.

 

a)What is the area between the graph of y=6f(x-6) and the x-axis?

b)What is the area between the graph of y=1/2f(-x) and the x-axis?

c)What is the area between the graph of y=f(x+2) and the x-axis?

 Oct 6, 2018
 #1
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a)What is the area between the graph of y=6f(x-6) and the x-axis?

 

The (x - 6) part just shifts the graph to the right by 6 units.....this does not change the area

The  "6"  part  makes every point on the graph 6 times as high..so the area  is

6 * 10   = 60 units^2

 

 

 

b)What is the area between the graph of y=1/2f(-x) and the x-axis?

The (-x)  part rotates the graph about the y axis....the area is unchanged

The (1/2) part makes every point on the graph 1/2 as high....so the area is

(1/2) * 10   =  5 units^2

 

c)What is the area between the graph of y=f(x+2) and the x-axis?

This just shifts the graph 2 uits to the left....the area is unchanged

 

 

cool cool cool

 Oct 6, 2018

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