https://file.aiquickdraw.com/mathbot/file/17302477773018lqa8i68.jpg

The question on the screen is asking for the missing value of \( f(x) \) when \( x = 1 \) for the function \( f(x) = 6(1.5)^x \).

To solve for \( f(1) \):

1. Substitute \( x = 1 \) into the function:
   \[
   f(1) = 6(1.5)^1
   \]

2. Calculate \( (1.5)^1 \), which is simply 1.5:
   \[
   f(1) = 6 \times 1.5
   \]

3. Multiply:
   \[
   f(1) = 9
   \]

Thus, the missing value at \( (1, ?) \) is **9**.

Would you like more details, or do you have any questions about this?

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Here are some related questions for further practice:

1. What would the value of \( f(2) \) be for this function?
2. How would the function change if the base of the exponent was 2 instead of 1.5?
3. Can you determine the initial value and growth rate from the function \( f(x) = 6(1.5)^x \)?
4. What is the general formula for exponential growth functions?
5. How would you graph an exponential function like \( f(x) = 6(1.5)^x \)?

**Tip:** For exponential functions, the base of the exponent (in this case, 1.5) determines if the function grows (if base > 1) or decays (if base < 1).

Find the missing value from the graph defining the function shown below. Note that the graph is not drawn to scale. f(x) = 6(1.5)^x, and you need to determine the value of f(1).

Learn how to find the missing value in the exponential function f(x) = 6(1.5)^x when x = 1. This problem covers core concepts of exponential functions and function evaluation, suitable for students in Grades 8-10.

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