The function h is defined as follows. h(x)=x-8/3x+6 Find h(6) .

Simplify your answer as much as possible. If applicable, click on "Undefined".

The given function is:

\[
h(x) = \frac{x - 8}{3x + 6}
\]

To find \( h(6) \), we substitute \( x = 6 \) into the function:

\[
h(6) = \frac{6 - 8}{3(6) + 6} = \frac{-2}{18 + 6} = \frac{-2}{24} = \frac{-1}{12}
\]

So, the value of \( h(6) \) is \( \frac{-1}{12} \).

Let me know if you want more details or have any questions! Here are 5 related questions to further your understanding:

1. How would you evaluate \( h(x) \) for other values of \( x \)?
2. What happens to the function as \( x \to \infty \)?
3. What is the domain of the function \( h(x) \)?
4. How would you find the inverse of \( h(x) \)?
5. How can you determine if \( h(x) \) has any asymptotes?

**Tip:** Always check the denominator of a rational function to avoid division by zero!

The function h is defined as follows. h(x)=x-8/3x+6. Find h(6). Simplify your answer as much as possible.

This problem guides you through finding h(6) for the rational function h(x) = (x - 8) / (3x + 6). Learn how to simplify rational expressions using substitution and explore key algebraic concepts. Suitable for students in Grades 9-11.

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