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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.

An exponential function is described by the equation h(x)=49(27)x
. Which inequality describes the range of this function?

(1 point)
Responses

y>0
y greater than 0

y≥0
y greater-than-or-equal-to 0

0<y<16
0 less than y less than 16

−∞<y<∞
negative infinity less than y less than infinity
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Answer 1

To analyze the given function \( h(x) = 49(27)^x \), we note that:

1. \( 49 \) is a positive constant.
2. The base \( 27 \) is also positive and greater than 1, indicating that the exponential function will increase as \( x \) increases.

Since \( (27)^x \) is always greater than 0 for any real number \( x \), it follows that \( h(x) \) is also positive for all \( x \):

\[ h(x) = 49(27)^x > 0 \]

Thus, the function does not touch or cross the x-axis, meaning there's no \( x \) for which \( h(x) \) is zero.

The range of the function can therefore be described by the inequality:

\[ y > 0 \]

So the correct response is:

y > 0