91Ó°ÊÓ

When we talk about function evaluation, we aim to find the output of a function for a specific input value. In the language of mathematics, this means plugging a value into a function and calculating the result.
For example, if you have a linear function like \( f(x) = 3x - 10 \), evaluating this function simply means determining what \( f(x) \) would be when we feed in a certain number, called the input.
• By evaluating functions, we uncover the relationship between input and output, which is the essence of any function.
• This concept is crucial in calculus and many applied fields, helping us predict outputs based on various scenarios.

The idea of substitution in mathematics is straightforward: replace one element with another. In our case, it involves taking the function \( f(x) = 3x - 10 \) and substituting \( x \) with a given number, such as 20.
This substitution step is key because it transforms the general equation into a specific expression that we can solve. - Start by identifying the 'x' in the function.- Replace 'x' with your specific number, here 20, transforming the equation into \( f(20) = 3 \times 20 - 10 \).
This step sets the stage for simplifying and solving the function, allowing us to compute a precise result.

Once we've substituted the number into our function, we need to simplify it. This is where the order of operations comes in, ensuring we perform calculations in a consistent and correct manner. - The order of operations is often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction).
In our example, \( f(20) = 3 \times 20 - 10 \), we must first multiply because multiplication comes before subtraction. This gives us:
1. Multiply: 3 times 20 equals 60. 2. Subtract: subtract 10 from 60 to get 50. - Correctly following these steps results in the function's value, here \( f(20) = 50 \). Understanding and applying the order of operations is fundamental as it keeps calculations orderly and accurate.