If f(x) = 2x² - 7x + 1 / 3x³ - 3 find f (-3)

To find \( f(-3) \) for the function:

\[
f(x) = \frac{2x^2 - 7x + 1}{3x^3 - 3}
\]

Substitute \( x = -3 \) into the function:

### Step 1: Calculate the numerator
The numerator is \( 2x^2 - 7x + 1 \).

For \( x = -3 \):
\[
2(-3)^2 - 7(-3) + 1 = 2(9) + 21 + 1 = 18 + 21 + 1 = 40
\]

### Step 2: Calculate the denominator
The denominator is \( 3x^3 - 3 \).

For \( x = -3 \):
\[
3(-3)^3 - 3 = 3(-27) - 3 = -81 - 3 = -84
\]

### Step 3: Compute \( f(-3) \)
Now, divide the numerator by the denominator:
\[
f(-3) = \frac{40}{-84} = \frac{40}{-84} = \frac{10}{-21}
\]

Thus, \( f(-3) = -\frac{10}{21} \).

Would you like further details or explanations?

Here are some related questions:
1. How would you find the derivative of \( f(x) \)?
2. What happens to \( f(x) \) as \( x \to \infty \)?
3. How would you determine where \( f(x) = 0 \)?
4. Can \( f(x) \) have vertical asymptotes? How can you find them?
5. How does changing the coefficient of \( x^2 \) in the numerator affect \( f(x) \)?

**Tip:** Always simplify fractions when solving rational functions to make your final answer clear.

If f(x) = 2x² - 7x + 1 / 3x³ - 3, find f(-3)

Learn how to evaluate the rational function f(x) = (2x² - 7x + 1) / (3x³ - 3) by finding f(-3). Follow a step-by-step process that covers calculating the numerator and denominator, substituting values, and simplifying the final expression. This example is suitable for students in Grades 10-12 and focuses on key algebraic concepts like substitution and rational functions.

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