Evaluating Functions

Evaluating a function means finding the output value (or result) of the function when a specific input value (or argument) is given.

Table of Contents:

• Evaluating Functions
• Formula for Evaluating Functions
• Solved Examples of Evaluating Function
• FAQs

Evaluating Functions

The process of evaluating a function involves substituting the input value for the function’s variable and simplifying the resulting expression.

For example, consider the function f(x) = 2x + 1. To evaluate the function at x = 3, we substitute 3 for x and simplify:

f(3) = 2(3) + 1 = 6 + 1 = 7

So, the value of the function f(x) when x = 3 is 7.

Similarly, consider the function g(x) = x^2 – 4x + 3. To evaluate the function at x = 2, we substitute 2 for x and simplify:

g(2) = 2^2 – 4(2) + 3 = 4 – 8 + 3 = -1

So, the value of the function g(x) when x = 2 is -1.

In general, to evaluate a function f(x) at a given value of x, substitute the value of x into the function and simplify the resulting expression to get the output value of the function.

Formula for Evaluating Functions

The formula for evaluating a function at a specific value of its independent variable is:

f(x) = function expression

To evaluate the function at a specific value, simply replace x in the function expression with the value you want to evaluate it at, and simplify the resulting expression.

For example, let’s say we want to evaluate the function f(x)= x^2 + 4x- 5 at x=4
f(4) = 4^4 + 3 (4) – 5
= 256 + 12 – 5
=264

So, the value of function f(x) at x = 4 is 264.

Solved Examples of Evaluating Function

Example 1: Evaluate the function f(x) = 3x – 4 at x = 5.

Solution: Using the formula for evaluating functions, we substitute x = 5 into the function expression and simplify:

f(5) = 3(5) – 4
= 15 – 4
= 11

Therefore, the value of the function f(x) at x = 5 is 11.

Example 2: Evaluate the function g(x) = 2x^2 + 5x – 3 at x = -2.

Solution: Using the formula for evaluating functions, we substitute x = -2 into the function expression and simplify:

g(-2) = 2(-2)^2 + 5(-2) – 3
= 2(4) – 10 – 3
= 8 – 10 – 3
= -5

Therefore, the value of the function g(x) at x = -2 is -5.

Example 3: Evaluate the function h(x) = sqrt(x + 4) – 2 at x = 3.

Solution: Using the formula for evaluating functions, we substitute x = 3 into the function expression and simplify:

h(3) = sqrt(3 + 4) – 2
= sqrt(7) – 2

Therefore, the value of the function h(x) at x = 3 is sqrt(7) – 2.

These are some examples of evaluating functions.

Evaluating Functions FAQS

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