f(x) = |x|
The given function is f(x) = |x|, which represents the absolute value of x
The given function is f(x) = |x|, which represents the absolute value of x.
To understand how the function behaves, let’s break it down into two cases:
1. When x is positive or zero (x ≥ 0): In this case, the absolute value of x is equal to x itself. So, when x is positive or zero, f(x) = x. This means that the graph of f(x) will be a straight line with a positive slope, passing through the origin (0, 0) and extending upwards.
2. When x is negative (x < 0): In this case, the absolute value of x is equal to the negation of x. So, when x is negative, f(x) = -x. This means that the graph of f(x) will be a straight line with a negative slope, passing through the origin (0, 0) and extending downwards. Combining these two cases, we can draw the graph of f(x). It will consist of two straight lines meeting at the origin with a corner point. The line on the right side of the origin (x ≥ 0) will have a positive slope, and the line on the left side (x < 0) will have a negative slope. To summarize, the graph of f(x) = |x| will be a "V-shaped" graph, symmetric with respect to the y-axis, and passing through the origin. The point where the two lines meet at the origin is called the vertex of the graph.
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