Understanding the Function f(x) = |x| – 2: Step-by-Step Breakdown and Graphing

f(x) = |x| – 2

To understand the function f(x) = |x| – 2, let’s break it down step by step

To understand the function f(x) = |x| – 2, let’s break it down step by step.

The symbol | | indicates the absolute value of a number. The absolute value of a number is its distance from zero on the number line, regardless of whether the number is positive or negative. For example, the absolute value of 5 is 5, and the absolute value of -5 is also 5. The absolute value is always non-negative (it is never less than zero).

So, f(x) = |x| – 2 means that we take the absolute value of x, and then subtract 2 from it.

To graph this function, we’ll start by making a table of values. Let’s choose some values for x and calculate the corresponding values for f(x).

Let’s choose x = -3:
f(x) = |(-3)| – 2
f(x) = 3 – 2
f(x) = 1

So, when x = -3, f(x) = 1.

Now let’s choose x = -2:
f(x) = |(-2)| – 2
f(x) = 2 – 2
f(x) = 0

When x = -2, f(x) = 0.

Continuing this process, we can generate more points for the table of values.

x |x| – 2
————–
-3 1
-2 0
-1 -1
0 -2
1 -1
2 0
3 1

Now, let’s plot these points on a graph.

On the x-axis, we mark the values -3, -2, -1, 0, 1, 2, and 3. On the y-axis, we mark the values -2, -1, 0, 1.

Plotting the points from the table, we get a “V-shaped” graph that opens upwards and touches the x-axis at (0, -2).

Hence, the graph of the function f(x) = |x| – 2 is a “V-shaped” graph with the vertex at (0, -2) and opens upwards.

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