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?

grif389
Oct 6, 2018

#1**+1 **

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

CPhill
Oct 6, 2018