The function r times x is equal to negative 0 point 0 0 0 3 4 5 times open paren x minus 50 close paren squared plus 2 point 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 times x is equal to 0 point 3 0 4 8 x Which composition can be used to model the curve of the road in terms of meters?
Answer
A
m times open paren r times x close paren is equal to negative 0 point 0 0 0 1 0 5 1 5 6 times open paren x minus 50 close paren squared plus 0 point 6 4 0 0 8
B
m times open paren r times x close paren is equal to negative 0 point 0 0 0 1 0 5 1 5 6 times open paren x minus 50 close paren squared plus 2 point 1
C
m times open paren r times x close paren is equal to negative 0 point 0 0 0 3 4 5 times open paren 0 point 3 0 4 8 x minus 50 close paren squared plus 2 point 1
D
m times open paren r times x close paren is equal to negative 0 point 0 0 0 3 4 5 times open paren 0 point 3 0 4 8 x minus 50 close paren squared plus 0 point 6 4 0 0 8
Explanation
To express the road curve’s height in meters, apply the conversion function m to the output of r. Since m(y) = 0.3048y, multiply both parts of r(x) by 0.3048: 0.3048(−0.000345) = −0.000105156 and 0.3048(2.1) = 0.64008. This gives m(r(x)) = −0.000105156(x − 50)² + 0.64008, which is choice A.
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