Understanding the Function f(x) = |x| + 2 | Step by Step Explanation and Graph Visualization

f(x) = |x| + 2

To understand the function f(x) = |x| + 2, let’s break it down step by step

To understand the function f(x) = |x| + 2, let’s break it down step by step.

1. The vertical bars, |x|, represent the absolute value of x. Absolute value is a mathematical function that returns the distance of a number from zero, regardless of its sign. For example, the absolute value of 3 is 3, and the absolute value of -3 is also 3.

2. In this function, we take the absolute value of x and then add 2 to the result. So, no matter whether x is positive or negative, we will always add 2 to its absolute value.

Let’s create a table of values to better understand the function:

x |x| f(x) = |x| + 2
————————–
-3 3 5
-2 2 4
-1 1 3
0 0 2
1 1 3
2 2 4
3 3 5

As you can see from the table, no matter what the value of x is, the function f(x) returns a value that is 2 units larger than the absolute value of x. This means that the graph of f(x) will always be a line that starts from the point (0,2) and increases by 1 unit for every unit increase in x, both to the left and right of the origin.

Visually, the graph will look like a “V” shape, with the vertex at (0,2). The line will have a positive slope of 1 and will extend indefinitely in both directions.

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