How to Evaluate a Rational Function

TL;DR

Evaluate F of x = 8/(4+x^2) at various values to understand the process.

Transcript

hello in this video we're going to do an example of evaluating a rational function so we have f of x equals 8 over 4 plus x squared we're going to find F of 0 f of 2 f of negative 2 and F of 14. let's go ahead and work through it solution let's start with f of zero F of 0 means that we have to evaluate F at zero we look at the formula for f of x wh... Read More

Key Insights

• 😑 Evaluating rational functions involves substituting values for variables and simplifying the expression.
• 🥺 The process of evaluating rational functions can lead to unique and interesting results.
• 😑 Simplify complex expressions step by step to reach final rational function values.

Questions & Answers

Q: How do you evaluate F of 0 for the given rational function?

To find F of 0, substitute 0 for x in the function f(x) = 8/(4+x^2), simplify the expression, and the result is 2.

Q: What is the value of F of 2 in the rational function?

For F of 2, substitute 2 into the function f(x) = 8/(4+x^2), simplify the expression, and the result is 1.

Q: Is F of -2 the same as F of 2 in the rational function?

Yes, F of -2 is the same as F of 2 in the given rational function, both yielding a value of 1 after substituting and simplifying.

Q: How do you simplify F of 14 in the rational function to a final value?

For F of 14, substitute 14 into the function f(x) = 8/(4+x^2), simplify the expression step by step or in one go, resulting in 1/25.

Summary & Key Takeaways

• Evaluate F of x = 8/(4+x^2) at x = 0, 2, -2, 14.

• For F of 0, substitute x with 0 to get 2.

• F of 2 is 1, F of -2 is 1, and F of 14 is 1/25 after simplification.