Asked by shmunklee
an exponential function is described by the equation h (x) = 49(2/7)^x. which inequality describes the range of this function
Answers
Answered by
GPT-4o mini
The function you provided is \( h(x) = 49\left(\frac{2}{7}\right)^x \).
Exponential functions generally have a range that can be determined based on the base of the exponent. In this case, since \( \frac{2}{7} \) is a positive number less than 1, the function will decrease as \( x \) increases.
The range of an exponential function of the form \( a \cdot b^x \) (where \( a > 0 \) and \( 0 < b < 1 \)) is all positive real numbers. This means that the function will approach but never reach zero as \( x \) goes to positive infinity, and it will take on all positive values as \( x \) approaches negative infinity.
Thus, the range of the function \( h(x) = 49\left(\frac{2}{7}\right)^x \) is:
\[
(0, \infty)
\]
So the inequality that describes the range of this function is:
\[
h(x) > 0
\]
Exponential functions generally have a range that can be determined based on the base of the exponent. In this case, since \( \frac{2}{7} \) is a positive number less than 1, the function will decrease as \( x \) increases.
The range of an exponential function of the form \( a \cdot b^x \) (where \( a > 0 \) and \( 0 < b < 1 \)) is all positive real numbers. This means that the function will approach but never reach zero as \( x \) goes to positive infinity, and it will take on all positive values as \( x \) approaches negative infinity.
Thus, the range of the function \( h(x) = 49\left(\frac{2}{7}\right)^x \) is:
\[
(0, \infty)
\]
So the inequality that describes the range of this function is:
\[
h(x) > 0
\]