To analyze the graphs based on the form $y = ab^x$, let's go through each question.

1. Which graph has the largest value for $b$?

   • In the equation $y = ab^x$, the parameter $b$ determines the growth or decay rate. If $b > 1$, the function grows exponentially, while if $0 < b < 1$, the function decays. Observing the graph, the green curve $G$ grows the fastest as $x$ increases, indicating that it has the largest value of $b$ (greater than 1).

2. Which graph has the smallest value for $b$?

   • The smallest value for $b$ would correspond to the function that decays the most rapidly. The blue curve $B$ is decreasing sharply as $x$ increases, indicating a $b$ value close to 0 but positive (between 0 and 1).

3. Which graph has the largest value for $a$?

   • The parameter $a$ in $y = ab^x$ represents the initial value when $x = 0$. Observing where each graph crosses the $y$-axis, the black curve $K$ has the highest $y$-intercept, indicating that it has the largest value of $a$.

Summary of Answers:

• Largest value of $b$: Green curve $G$.
• Smallest value of $b$: Blue curve $B$.
• Largest value of $a$: Black curve $K$.

Would you like further clarification on any of these points?

Here are some follow-up questions to deepen your understanding:

1. What effect would a negative exponent have on the growth or decay of these functions?
2. How would the graph change if $a$ were negative?
3. What happens to the graph as $b$ approaches 1?
4. How would a graph look if $b$ were exactly equal to 1?
5. Can two different functions $y = ab^x$ and $y = cd^x$ intersect more than once?

Tip: Remember that in exponential functions, $b$ controls the direction and rate of growth or decay, while $a$ influences the starting value at $x = 0$.