Select the correct answer.Which graph shows an exponential function that nears a constant value as x approaches positive infinity and has a y-inte

To select the correct answer for the graph displaying an exponential function that approaches a constant value as $x$ approaches positive infinity and has a y-intercept, we need to look for key characteristics of exponential functions.

1. Exponential Function Behavior:

   • Exponential functions can take forms such as $y = a \cdot b^x$, where:
     • $a$ is the y-intercept (when $x = 0$).
     • $b$ determines the growth or decay.
   • For the function to approach a constant value as $x$ approaches positive infinity, we typically consider functions that have a horizontal asymptote.

2. Horizontal Asymptote:

   • If the function approaches a constant value $L$, it would resemble forms like $y = L + a \cdot e^{-bx}$ or $y = L + a \cdot b^{-x}$ for certain values of $a$ and $b$, where $b > 1$ indicates decay.

3. Y-Intercept:

   • The y-intercept will be the value of the function when $x = 0$.

Given these points, check each graph to identify:

• Which graph moves closer to a horizontal line (indicating that it approaches a constant value).
• Identify the y-intercept from the graph.

Final Answer

The correct choice will be the graph that shows an exponential decay approach towards a horizontal line as $x$ increases, with a clear y-intercept value at $x = 0$.