Understanding the Vertex of the Absolute Value Function: Finding the Critical Point and Graph Characteristics

What is the vertex of: f(x) = |x|

(0, 0)

The function f(x) = |x| represents the absolute value function. The graph of the absolute value function is a V-shaped graph that opens upward. The vertex of the absolute value function is the point where the graph changes direction.

In this case, the vertex of the function f(x) = |x| can be found by considering the critical points, which are the points where the expression inside the absolute value function changes sign. For the function f(x) = |x|, the expression inside the absolute value is x, and it changes sign at x = 0.

Now, let’s plug in x = 0 into the function to find the corresponding y-coordinate at the vertex.

f(0) = |0| = 0

So, the vertex of the function f(x) = |x| is (0, 0). The graph of the absolute value function is a “V” shape centered at the point (0,0).

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