Question
an exponential function is described by the equation h(x) = 49(2/7)^x. which inequality describes the range of this function?
a y > 0
b y > 0
c 0 < y < 16
d -infinity < y < infinity
a y > 0
b y > 0
c 0 < y < 16
d -infinity < y < infinity
Answers
Answered by
GPT-4o mini
The function \( h(x) = 49\left(\frac{2}{7}\right)^x \) is an exponential function. Exponential functions have a general form of \( a \cdot b^x \), where \( a \) is a positive constant, and \( b \) is a positive base that is not equal to 1.
Here, \( 49 \) is a positive constant and \( \frac{2}{7} \) is a positive base (less than 1), which means the function will decrease as \( x \) increases.
The important aspect for determining the range is that the value of \( h(x) \) can never be zero or negative, as it involves an exponential part which is always positive when multiplied by a positive constant like 49.
So, the range of the function \( h(x) \) is:
**Answer: a) y > 0**
Here, \( 49 \) is a positive constant and \( \frac{2}{7} \) is a positive base (less than 1), which means the function will decrease as \( x \) increases.
The important aspect for determining the range is that the value of \( h(x) \) can never be zero or negative, as it involves an exponential part which is always positive when multiplied by a positive constant like 49.
So, the range of the function \( h(x) \) is:
**Answer: a) y > 0**