Understanding the Vertex of Absolute Value Functions: Explained with f(x) = |x – 4|

What is the vertex of: f(x) = |x – 4|

(4, 0)

To find the vertex of the function f(x) = |x – 4|, we first need to understand what the vertex represents in absolute value functions.

An absolute value function is represented as f(x) = |x – h| + k, where (h, k) is the vertex of the function. The vertex represents the point on the graph where the function reaches its minimum or maximum value, depending on the orientation of the graph.

In the given function f(x) = |x – 4|, we can see that the “h” value is 4. This means that the graph will be shifted horizontally by 4 units. However, notice that there is no “k” value in this function. This implies that the graph of the given function will not be shifted vertically, and we can consider the “k” value to be 0.

So, the vertex of f(x) = |x – 4| is (4, 0). This point represents the minimum value of the function, as the vertex in an absolute value function corresponds to the lowest point on the graph.

More Answers:
Analyzing the Properties and Behavior of the Exponential Function f(t) = Ae^(kt)
Understanding the Vertex of the Absolute Value Function: Finding the Critical Point and Graph Characteristics
Finding the Vertex of the Function f(x) = |x| – 4: Explained and Illustrated

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