To analyze this question, let’s break down the characteristics of exponential functions in the form $y = ab^x$:

1. Parameter $b$: Controls the growth or decay rate. If $b > 1$, the function represents exponential growth. The larger the $b$, the steeper the graph's growth as $x$ increases. If $0 < b < 1$, it represents exponential decay, where the graph falls towards the x-axis as $x$ increases.

2. Parameter $a$: This is the initial value or vertical stretch factor of the function when $x = 0$. A larger $a$ shifts the graph upwards without affecting the growth rate.

Answering the Questions:

1. Graph with the Largest Value for $b$:

   • The graph with the steepest positive slope (rapid growth) has the largest $b$. From the image, the yellow curve (labeled $O$) shows the most rapid growth, indicating the largest $b$ value.

2. Graph with the Smallest Value for $b$:

   • The smallest $b$ corresponds to the graph that decays the fastest if $0 < b < 1$, or the one that grows the slowest among the growth functions. Here, the blue curve (labeled $B$) is decaying the fastest, suggesting it has the smallest $b$ value, possibly indicating it’s less than 1.

3. Graph with the Largest Value for $a$:

   • The graph with the highest starting point at $x = 0$ will have the largest $a$. From observation, the green curve (labeled $G$) starts the highest on the y-axis, indicating it has the largest $a$ value.

Summary of Answers:

• Largest $b$: Yellow curve ($O$)
• Smallest $b$: Blue curve ($B$)
• Largest $a$: Green curve ($G$)

Would you like a deeper explanation of exponential functions, or do you have any specific questions?

Here are some related questions to expand your understanding:

1. How does changing $a$ affect the graph’s appearance without altering $b$?
2. What happens to the graph if $b = 1$?
3. How would negative values for $b$ impact the function $y = ab^x$?
4. If $b$ is very close to 1, how would the graph look compared to when $b$ is significantly greater than 1?
5. Can exponential functions with the same $b$ but different $a$ values intersect?

Tip: Exponential functions with larger bases grow faster, but their initial values still play a key role in determining their position on the graph.