For the function f(x)=8−x3x2−4
 answer each of the following questions.

Evaluate the function at the following values of x 

compute (accurate to 8 decimal places).

(i) 2.5
   

             f(x)=
 Answer 1 Question 1

(ii) 2.01
   

             f(x)=
 Answer 2 Question 1



To evaluate the function \( f(x) = \frac{8 - x}{3x^2 - 4} \) at the given values of \( x \), we substitute \( x = 2.5 \) and \( x = 2.01 \) into the equation.

### 1. Evaluating \( f(2.5) \):
\[
f(2.5) = \frac{8 - 2.5}{3(2.5)^2 - 4}
\]
Calculate the numerator and the denominator separately:

- Numerator: \( 8 - 2.5 = 5.5 \)
- Denominator: \( 3(2.5)^2 - 4 = 3(6.25) - 4 = 18.75 - 4 = 14.75 \)

Thus:
\[
f(2.5) = \frac{5.5}{14.75} \approx 0.37288136
\]

### 2. Evaluating \( f(2.01) \):
\[
f(2.01) = \frac{8 - 2.01}{3(2.01)^2 - 4}
\]
Calculate the numerator and the denominator separately:

- Numerator: \( 8 - 2.01 = 5.99 \)
- Denominator: \( 3(2.01)^2 - 4 = 3(4.0401) - 4 = 12.1203 - 4 = 8.1203 \)

Thus:
\[
f(2.01) = \frac{5.99}{8.1203} \approx 0.73771277
\]

### Answers:

(i) \( f(2.5) \approx 0.37288136 \)

(ii) \( f(2.01) \approx 0.73771277 \)

Would you like further details or have any questions?

Here are five additional related questions:
1. What is the domain of the function \( f(x) = \frac{8 - x}{3x^2 - 4} \)?
2. What happens to \( f(x) \) as \( x \) approaches 0?
3. Can we find the asymptotes of \( f(x) \)? If so, what are they?
4. How would you determine if the function has any points of discontinuity?
5. What is the behavior of \( f(x) \) as \( x \to \infty \)?

**Tip:** When evaluating functions, always calculate the numerator and denominator separately for clarity and accuracy.

For the function f(x) = (8 − x) / (3x^2 − 4), answer each of the following questions. Evaluate the function at the following values of x: (i) 2.5, (ii) 2.01.

Learn how to evaluate the rational function f(x) = (8 − x) / (3x^2 − 4) at specific values of x, including 2.5 and 2.01, with a step-by-step solution. This algebra problem explores rational functions and is suitable for students in Grades 9-12.

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