Graphing the Absolute Value Function: Step-by-Step Guide and Examples

f(x) = |x| + 2

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

Step 1: Understanding the Absolute Value Function
The function |x| represents the absolute value of x, which means it returns the distance of x from zero on the number line

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

Step 1: Understanding the Absolute Value Function
The function |x| represents the absolute value of x, which means it returns the distance of x from zero on the number line. For positive numbers, the absolute value remains the same, while for negative numbers, it becomes positive. For example, |5| = 5, |-3| = 3.

Step 2: Adding 2
The expression |x| + 2 adds 2 to the absolute value of x. This shifts the graph of the absolute value function upward by 2 units.

Step 3: Graphing the Function
To graph the function f(x) = |x| + 2, follow these steps:

1. Determine the basic shape of the absolute value function, which is a “V” shape.
2. Shift the graph 2 units up to account for the +2 term.
3. Locate key points on the graph:

– When x = 0, the absolute value is 0. Therefore, f(0) = |0| + 2 = 2. This gives us the point (0, 2).
– When x = 1, the absolute value is 1. Therefore, f(1) = |1| + 2 = 3. This gives us the point (1, 3).
– When x = -1, the absolute value is 1. Therefore, f(-1) = |-1| + 2 = 3. This gives us the point (-1, 3).

4. Plot these points on the coordinate plane.
5. Draw a “V” shape connecting the points.

The resulting graph of f(x) = |x| + 2 is a “V” shape with the vertex at (0, 2) and opening upward. The graph intersects the y-axis at (0, 2), and the x-axis at (-2, 0) and (2, 0).

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