function and function notation using the variable x and explain how we evaluate a function for a given x
A function is a mathematical relationship between two variables, typically denoted as "x" and "y". It takes an input value, represented by "x", and produces an output value, represented by "y". The function notation is commonly written as f(x).
To define a function, you need an equation or a rule that describes how the input "x" relates to the output "y". Here's an example:
Let's say we have a function that multiplies an input value by 3 and adds 2. We can express it as: f(x) = 3x + 2
To evaluate a function for a given value of "x", you simply substitute that value into the function and perform the necessary calculations. Here are the steps to evaluate the function f(x) = 3x + 2 for a specific value of "x":
1. Identify the given value of "x".
2. Replace "x" in the function with the given value.
3. Perform the calculation, following the order of operations (PEMDAS/BODMAS).
Let's work through an example. Suppose you want to evaluate the function f(x) = 3x + 2 for x = 4.
Step 1: Given value of "x": x = 4
Step 2: Replace "x" in the function: f(4) = 3(4) + 2
Step 3: Perform the calculation: f(4) = 12 + 2 = 14
So, when x = 4, the function f(x) evaluates to 14.