Finding the Vertex of the Function f(x) = |x| – 4: Explained and Illustrated

What is the vertex of: f(x) = |x| – 4

(0, -4)

To find the vertex of the given function f(x) = |x| – 4, we need to understand that the absolute value function |x| has a “V” shape and is symmetrical about the y-axis. The vertex of this function occurs at the bottom of the “V” shape.

The vertex can be found by determining where the minimum value of the function occurs. We know that |x| is always non-negative, so the smallest possible value of |x| is 0. Therefore, we need to find the value of x that makes |x| equal to 0.

Solving the equation |x| = 0, we see that x = 0. Substituting x = 0 back into the original function f(x) = |x| – 4 gives us f(0) = |0| – 4 = 0 – 4 = -4.

Hence, the vertex of the function f(x) = |x| – 4 is (0, -4). The graph of the function will have a downward “V” shape and the vertex will be located at the point (0, -4).

More Answers:
Understanding Monotonic Functions: Definition, Examples, and Applications in Mathematics
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

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