Question

An airplane’s altitude in feet during its descent for landing can be found using the function f(x) = −300x + 30,000, where x represents the horizontal distance in miles from where the plane begins its descent. After new government regulations become law, the airplane’s

descent will be modeled by the function g(x) = −300x + 30,500. Which statement describes this change?


A. The airplane descends 500 feet per horizontal mile slower
B. The airplane starts its descent from an altitude 500 feet higher
C. The airplane descends 500 feet per horizontal mile faster
D. The airplane starts its descent from an altitude 500 feet lower

Answer 1

B. The airplane starts its descent from an altitude 500 feet higher

Explanation:

f(x) = −300x + 30,000

the function itself represents the airplane's altitude. the y intercept, 30,000 ft, then represents the initial starting position of the plane.

when it changes

g(x) = −300x + 30,500

only the y intercept changes. it's now 30,500 ft, which is 500 more than before. that means the plane initial position is 500 feet higher.

since the term with x doesn't change, the rate will not be affected. the answers with slower or faster talks about rate, which isn't what changed.