https://file.aiquickdraw.com/mathbot/file/1725507096190i1dki1dd.jpg

The problem in the image asks for the value of \( f(0) \) where the function \( f(u) \) is defined as:

\[
f(u) = \frac{2u^2 + 7u - 18}{u^2 - 8u + 7}
\]

We need to substitute \( u = 0 \) into the function and simplify.

### Step-by-step solution:

1. **Substitute \( u = 0 \) into the numerator:**
   \[
   2(0)^2 + 7(0) - 18 = -18
   \]

2. **Substitute \( u = 0 \) into the denominator:**
   \[
   (0)^2 - 8(0) + 7 = 7
   \]

3. **Simplify the expression:**
   \[
   f(0) = \frac{-18}{7}
   \]

Thus, \( f(0) = -\frac{18}{7} \).

Do you want more details or have any questions?

Here are 5 related questions to deepen understanding:
1. What is the domain of \( f(u) \)?
2. How would you find the asymptotes of \( f(u) \)?
3. Can you factor the numerator and denominator of \( f(u) \)?
4. What is the value of \( f(1) \)?
5. How would you compute the limit of \( f(u) \) as \( u \to \infty \)?

**Tip:** Always check for undefined points in rational functions by analyzing when the denominator equals zero.

Find f(0) for the function f(u) = (2u^2 + 7u - 18) / (u^2 - 8u + 7).

This problem involves evaluating the rational function f(u) = (2u^2 + 7u - 18) / (u^2 - 8u + 7) at u = 0. Follow a step-by-step guide to substitute values and simplify the expression. Suitable for students in Grades 9-12 studying algebra and rational functions.

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