Use the graph of the function f(x) = (0.3)x to complete the sentence.

The graph of the function f(x) = (0.3)x has a

y-intercept at ( 
 , 
 ) and a horizontal asymptote at y = 
 .

The function \( f(x) = 0.3^x \) is an exponential function with a base less than 1, which means it decays as \( x \) increases. 

To complete the sentence:

The graph of the function \( f(x) = 0.3^x \) has a:

- **y-intercept** at \( (0, 1) \) because \( f(0) = 0.3^0 = 1 \).
- **horizontal asymptote** at \( y = 0 \), as the function approaches zero but never actually reaches it when \( x \to \infty \).

Would you like more details on how exponential functions work?

Here are 5 questions to expand on this:

1. How do you find the y-intercept of any exponential function?
2. What is the significance of the base in exponential functions?
3. How does the graph of \( f(x) = a^x \) change when \( 0 < a < 1 \)?
4. Can you explain why the horizontal asymptote is always at \( y = 0 \) for these types of functions?
5. What happens to the graph of \( f(x) = 0.3^x \) as \( x \) becomes negative?

**Tip:** In exponential functions, if the base is between 0 and 1, the function represents exponential decay.

Use the graph of the function f(x) = (0.3)x to complete the sentence. The graph of the function f(x) = (0.3)x has a y-intercept at ( , ) and a horizontal asymptote at y = .

Learn how to analyze the graph of the exponential function f(x) = 0.3^x. This problem explains how to find the y-intercept and the horizontal asymptote, touching on core concepts of exponential decay. Suitable for students in Grades 9-10.

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