Question

Determine the range of the exponential function f(x) = 3(1/2)^x − 6
.

(1 point)
Responses

y>6

y greater than 6

y≥−6

y greater-than-or-equal-to negative 6

y<−6

y less than negative 6

y>−6

y greater than negative 6

Answer 1

y > −6

Reason: 3(1/2)^x is always positive and approaches 0 as x → ∞, so f(x) = 3(1/2)^x − 6 approaches −6 from above but never equals it. As x → −∞, f(x) → ∞. Thus the range is (−6, ∞).