Question

Use the image to answer the question.

A curve with arrows at both the ends facing upward is plotted on a coordinate plane with x and y axes ranging from negative 10 to 10 in unit increments.
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The equation of the curve is f left parenthesis x right parenthesis equals 3 left parenthesis one half right parenthesis superscript x baseline minus 6. The coordinates through which the curve passes through are left parenthesis negative 2.5 comma 10 right parenthesis, left parenthesis negative 2 comma 6 right parenthesis, left parenthesis negative 1 comma 0 right parenthesis, left parenthesis 0 comma negative 3 right parenthesis, left parenthesis 6 comma negative 6 right parenthesis, and left parenthesis 10 comma negative 6 right parenthesis. Points are approximate.


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 negative 6

y≥−6

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

y<−6

y less than negative 6

Answer 1

(1/2)^x > 0 for all real x, so f(x) = 3(1/2)^x − 6 > −6. As x → ∞, f → −6 from above; as x → −∞, f → ∞.

Range: y > −6.