Question 10 • (OC27) MATH COLL ALGEBRA-1200710-S1-Degele-VOL7006P
The function r(x) = –0.000345(x – 50)2 + 2.1 can be used to model the curve of a road designed to allow for water to run off in rainstorms depending on the distance from the shoulder of the road, x, in feet. A European firm studying these curves is going to convert feet to meters using the function m(x) = 0.3048x.
Answer
A
m(r(x)) = –0.000105156(x – 50)2 + 2.1
B
m(r(x)) = –0.000105156(x – 50)2 + 0.64008
C
m(r(x)) = –0.000345(0.3048x – 50)2 + 2.1
D
m(r(x)) = –0.000345(0.3048x – 50)2 + 0.64008
Explanation
To find m(r(x)), substitute r(x) into m(x) = 0.3048x, so multiply the entire expression for r(x) by 0.3048. This gives −0.000345(0.3048)(x − 50)² + 2.1(0.3048) = −0.000105156(x − 50)² + 0.64008, which is choice B.
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