Understanding the Absolute Value Function and Evaluating f(x) = |x| – 2

f(x) = |x| – 2

Let’s break down the function f(x) = |x| – 2

Let’s break down the function f(x) = |x| – 2.

First, let’s define what the absolute value function, denoted as |x|, means. The absolute value of a number x is the distance that number is from zero on the number line. It always returns a non-negative value. For example, |5| = 5, since 5 is five units away from zero on the number line, and |-3| = 3, since -3 is also three units away from zero on the number line.

Now, let’s look at the given function f(x) = |x| – 2. This means that we are taking the absolute value of the input x, and subtracting 2 from it.

To evaluate this function, we substitute different values for x and simplify:

For example, let’s evaluate f(3):
f(3) = |3| – 2
= 3 – 2
= 1

Similarly, let’s evaluate f(-4):
f(-4) = |-4| – 2
= 4 – 2
= 2

You can continue evaluating the function for different values of x.

In general, the function f(x) = |x| – 2 will create a downward “V” shape graph. It will intersect the x-axis at x = 2, because at that point, f(x) will equal 0. For any x values greater than 2, f(x) will be positive, and for any x values less than 2, f(x) will be negative.

I hope this helps! Let me know if you have any further questions.

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