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The question asks: "On a graph, the value of *a* for a simple exponential function can be found at which coordinates?"

For a simple exponential function of the form \( f(x) = a \cdot b^x \), the constant *a* represents the **initial value** of the function, which is the function's value when \( x = 0 \). This means that the point where the graph of the function crosses the y-axis is at \( (0, a) \), since at \( x = 0 \), the function equals \( f(0) = a \).

Therefore, the correct answer is:
- \( (0, a) \)

Would you like more details or have any questions? Here are five related questions to expand your understanding:

1. What does the base \( b \) represent in an exponential function?
2. How does changing the value of *a* affect the graph of an exponential function?
3. What is the difference between exponential growth and decay?
4. How do you find the y-intercept of other types of functions, like quadratic or linear?
5. What is the horizontal asymptote of an exponential function, and how does it relate to *a*?

**Tip:** In an exponential function \( f(x) = a \cdot b^x \), \( a \) controls the vertical stretch or compression, while \( b \) controls the growth or decay rate.

On a graph, the value of a for a simple exponential function can be found at which coordinates?

Understand where to find the value of 'a' in a simple exponential function graph. This explanation covers exponential functions of the form f(x) = a * b^x and how the y-intercept (0, a) represents the initial value. Suitable for students in Grades 9-11.

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