Question
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<∞
negative infinity less than y less than infinity
0<y<16
0 less than y less than 16
y≥0
y greater-than-or-equal-to 0
y>0
. Which inequality describes the range of this function?
(1 point)
Responses
−∞<y<∞
negative infinity less than y less than infinity
0<y<16
0 less than y less than 16
y≥0
y greater-than-or-equal-to 0
y>0
Answers
GPT-4o mini
The exponential function described by the equation \( h(x) = 49(27)^x \) is a transformation of the basic exponential function \( a^x \), where \( a > 1 \). Since \( 27^x \) will yield positive values for all real \( x \) and is multiplied by 49 (a positive constant), the function's output, \( h(x) \), will also be positive for all inputs.
Therefore, as \( x \) approaches negative infinity, \( h(x) \) approaches 0, but never actually reaches 0. As \( x \) increases, \( h(x) \) will grow larger without bound.
Thus, the range of \( h(x) \) can be described by the inequality \( y > 0 \).
The correct response is:
**y > 0**.
Therefore, as \( x \) approaches negative infinity, \( h(x) \) approaches 0, but never actually reaches 0. As \( x \) increases, \( h(x) \) will grow larger without bound.
Thus, the range of \( h(x) \) can be described by the inequality \( y > 0 \).
The correct response is:
**y > 0**.