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

Question

a. -∞ < y < ∞
b. o < y < 16
c. y >= 0
d. y > 0

Answer 1

To determine the range of the exponential function given by the equation \( h(x) = 49\left(\frac{2}{7}\right)^x \), we need to consider the behavior of the function as \( x \) varies.

1. Identify the base of the exponential function: The base here is \( \frac{2}{7} \), which is between 0 and 1. As \( x \) increases, \( \left(\frac{2}{7}\right)^x \) approaches 0 but never actually reaches 0.

2. Evaluate the function at specific points:

   • For \( x = 0 \): \[ h(0) = 49\left(\frac{2}{7}\right)^0 = 49(1) = 49 \]
   • As \( x \) approaches \( \infty \): \[ h(x) \to 49(0) = 0 \]

3. Range of the function: Since \( h(x) \) decreases from \( 49 \) to \( 0 \) but never actually reaches \( 0 \), the function can take any positive value but cannot equal 0.

Given this analysis, the correct inequality describing the range of the function is:

d. \( y > 0 \).

This means the output of the function is always positive.