the absolute value function written as a piecewise function is:
f(x) = x + 8 if x ≥ -8
f(x) = -(x + 8) if x + < -8
How can this function be written as a piecewise function?
The absolute value function:
y = |x|
works as follows:
- y = x if x ≥ 0.
- y = -x if x < 0.
That is a piecewise function.
Now, in our case:
f(x) = |x + 8| can be rewritten to:
f(x) = x + 8 if (x + 8) ≥ 0
f(x) = -(x + 8) if (x + 8) < 0.
Now we should simplify the inequalities, so we get:
f(x) = x + 8 if x ≥ -8
f(x) = -(x + 8) if x + < -8
Here we have the absolute value function written as a piecewise function.
If you want to learn more about absolute value functions:
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