The function has a minimum at x = 0, hence it is neither always increasing nor decreasing.
The function f(x) = x^2 - 4 is:
Practice Questions
Q1
The function f(x) = x^2 - 4 is:
Always increasing
Always decreasing
Neither increasing nor decreasing
Both increasing and decreasing
Questions & Step-by-Step Solutions
The function f(x) = x^2 - 4 is:
Step 1: Identify the function given, which is f(x) = x^2 - 4.
Step 2: Recognize that this is a quadratic function, which typically has a U-shaped graph.
Step 3: Find the vertex of the function, which is the point where the function reaches its minimum or maximum value.
Step 4: For the function f(x) = x^2 - 4, the vertex occurs at x = 0.
Step 5: Calculate the value of the function at the vertex: f(0) = 0^2 - 4 = -4.
Step 6: Since the vertex is a minimum point, the function decreases until x = 0 and then increases after x = 0.
Step 7: Conclude that the function is not always increasing or always decreasing because it changes direction at x = 0.
Quadratic Functions – Understanding the properties of quadratic functions, including their shape (parabola), vertex, and behavior (increasing/decreasing intervals).
Minimum and Maximum Points – Identifying the minimum or maximum points of a function and understanding their significance in determining the function's behavior.
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