Determine if the function is bounded above, bounded below, bounded on its domain, or unbounded on its domain.
-$$y = 4 ^ { - x } + 6$$
A) Bounded above
B) Bounded below
C) Bounded
D) Unbounded

Question

Quizplus · Accepted Answer

The function $y = 4^{-x} + 6$ is bounded below because as $x$ increases, $4^{-x}$ approaches 0, making the function approach a minimum value of 6. It is not bounded above because as $x$ becomes very negative, $4^{-x}$ increases without bound, making the function unbounded above.

Determine If the Function Is Bounded Above, Bounded Below, Bounded y=4−x+6y = 4 ^ { - x } + 6y=4−x+6

Determine If the Function Is Bounded Above, Bounded Below, Bounded $y = 4 ^ { - x } + 6$