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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