Question

Use the image to answer the question.

A descending curve is graphed in quadrant 1 of a coordinate plane. The points left parenthesis 1 comma 14 right parenthesis and left parenthesis 2 comma 4 right parenthesis are plotted on the curve. The curve descends to but does not cross the x-axis.
The x-axis ranges from 0 to 10 in increments of 2. The y-axis ranges from 0 to 12 in increments of 2.


An exponential function is described by the equation h(x)=49(2/7)^(x) . Which inequality describes the range of this function?

(1 point)
Responses

0<y<16

0 less than y less than 16

y>0

y greater than 0

−∞<y<∞

negative infinity less than y less than infinity

y≥0

y greater-than-or-equal-to 0

Answer 1

h(x)=49(2/7)^x is always positive (49>0 and (2/7)^x>0). As x→∞, h(x)→0+ but never reaches 0; as x→−∞, h(x)→∞. So the range is y>0.