Graph of the Function f(x) = |x| – 2: Cases, Visualization, and Analysis

f(x) = |x| – 2

To find the graph of the function f(x) = |x| – 2, you’ll need to consider different cases depending on the value of x

To find the graph of the function f(x) = |x| – 2, you’ll need to consider different cases depending on the value of x.

First, let’s consider the case when x is greater than or equal to 0. In this case, the absolute value of x is equal to x. Therefore, f(x) = |x| – 2 simplifies to f(x) = x – 2.

Next, let’s consider the case when x is less than 0. In this case, the absolute value of x is equal to -x. Therefore, f(x) = |x| – 2 simplifies to f(x) = -x – 2.

Now, let’s plot the graph of f(x) = x – 2 for x ≥ 0. This is simply a straight line with a slope of 1 and a y-intercept of -2.

For the values of x < 0, let's plot the graph of f(x) = -x - 2. This is also a straight line, but with a slope of -1 and a y-intercept of -2. Now, let's combine both cases and plot the complete graph of f(x) = |x| - 2. When x ≥ 0, the graph of f(x) is a straight line with a slope of 1 and a y-intercept of -2. When x < 0, the graph of f(x) is a straight line with a slope of -1 and a y-intercept of -2. At x = 0, the graph discontinuity occurs, and the two lines meet at a single point. Here is a visualization of the graph of f(x) = |x| - 2: ___ | / | / | / __________|/___________ -3 -2 -1 0 1 2 3 The graph starts at (0, -2) and extends in both directions as straight lines with a slope of 1 until x = 0, where it meets the line with a slope of -1. The graph continues as a straight line with a slope of -1 for x < 0, intersecting the y-axis at (0, -2) and extending further downwards. Note: The absolute value function |x| removes any negative sign from x, so it ensures that the function f(x) is always non-negative.

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