Evaluate f(3)

Introduction

The function f(x) is a fundamental mathematical concept with wide-ranging applications in various fields. Evaluating f(3) involves substituting the value x = 3 into the function and calculating the resulting output.

Mathematical Definition

The function f(x) is defined as a rule that assigns to each input value x a corresponding output value y. The notation f(3) represents the output value obtained when x is replaced by 3.

Evaluating f(3)

To evaluate f(3), we need the specific function definition. Suppose we have the function f(x) = x^2 + 2x - 1. Substituting x = 3 into the function, we get:

f(3) = 3^2 + 2(3) - 1
f(3) = 9 + 6 - 1
f(3) = 14

Therefore, the value of f(3) is 14.

Applications of f(3)

The evaluation of f(3) finds practical applications in numerous areas:

In Physics

• Projectile Motion: f(3) can represent the height of a projectile after 3 seconds, given the initial velocity and launch angle.
• Simple Harmonic Motion: f(3) can provide the displacement of an object in a sinusoidal motion at a specific time point.

In Finance

• Compound Interest: f(3) can calculate the future value of an investment after 3 years, with a given interest rate compounded annually.
• Loan Repayment: f(3) can determine the monthly payment amount for a loan with a specific interest rate and loan term, considering the third payment.

In Computer Science

• Polynomial Interpolation: f(3) can be used as a data point to construct a polynomial curve fitting a set of given values.
• Numerical Integration: f(3) can serve as a point in a numerical integration scheme to approximate the area under a curve.

Statistics

• Probability Distribution: f(3) can represent the probability of an event occurring under a given probability distribution function.
• Confidence Intervals: f(3) can help estimate the confidence interval for a population parameter, based on a sample.

Tables for Evaluating f(3)

Effective Strategies for Evaluating f(3)

• Direct Substitution: Replace x with 3 in the function definition and calculate the result.
• Graphing: Graph the function and locate the y-coordinate corresponding to x = 3.
• Numerical Methods: Use numerical techniques such as the Newton-Raphson method to approximate the value of f(3).
• Casio Calculator: Utilize a graphing calculator to evaluate f(3) directly.

Step-by-Step Approach

1. Identify the function definition f(x).
2. Substitute x = 3 into the function.
3. Perform the necessary calculations to obtain the output value.
4. Report the value of f(3).

Conclusion

Evaluating f(3) is a fundamental mathematical operation that has wide-ranging applications in various disciplines. Understanding the techniques and strategies for evaluating f(3) is essential for solving problems and making informed decisions in these fields.

Call to Action

Put your knowledge to the test! Try evaluating f(3) for other functions, such as f(x) = x^3 - 2x^2 + 5x - 6 or f(x) = cos(x) + 1.