Understanding the Absolute Value Function | Graphing f(x) = |x – 2| + 1

f(x) = |x – 2| + 1

The function f(x) = |x – 2| + 1 is an example of an absolute value function

The function f(x) = |x – 2| + 1 is an example of an absolute value function. To understand it better, let’s break it down.

The absolute value function |x| returns the distance between x and 0 on the number line, always giving a non-negative value. In this case, we have |x – 2|, which means we are taking the distance between x and 2.

Next, we add 1 to the absolute value function. This means that the entire graph of the absolute value function is shifted upward by 1 unit.

So, the overall effect of f(x) = |x – 2| + 1 is to take the distance between x and 2, and then shift the graph upward by 1 unit.

To graph this function, you can start by drawing the graph of the absolute value function y = |x – 2|. The vertex or “corner point” of this graph is at (2, 0). From this point, the graph “bounces back” and extends infinitely in both directions.

Then, you can shift the entire graph upward by 1 unit. This means every y-value is increased by 1. So, the new vertex or corner point of the graph will be at (2, 1).

Overall, the graph of f(x) = |x – 2| + 1 is a V-shaped graph with its vertex at point (2, 1), and it extends infinitely in both directions.

Here’s a rough sketch of the graph:

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1 ___|___
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—|—|— x
2 3

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I hope this explanation helps! If you have any further questions or need more clarification, please let me know.

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