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Answer:
(a) $2.857 million
(b) vertical compression by 1/3; shift left by 6; shift up by 2
Step-by-step explanation:
(a) Find the year difference (2021-2010=11) and put that value where x is. Then do the arithmetic.
g(11) = (∛(11+6))/3 +2 = (∛17)/3 +2 ≈ 2.57128/3 +2 ≈ 0.857 +2
g(11) ≈ 2.857 . . . 2021 revenue in millions of dollars
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(b) For parent function f(x), the transformation ...
g(x) = a·f(x -h) +k
represents a vertical scaling by a factor of 'a', right shift by h units, and up shift by k units.
Comparing this form to the given g(x), we see ...
a = 1/3 . . . vertical compression by a factor of 1/3
h = -6 . . . .right shift 6 units
k = 2 . . . . up shift 2 units
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Additional comment
The vertical scaling is called "compression" when the scale factor is less than 1, and "stretch" when the scale factor is greater than 1. Here, the scale factor of 1/3 means the graph is vertically compressed.
