Question

Let f(x) = |x| / x , where x can be any real number except 0.

d. Express f as a piecewise function.

Answer 1

Answer: Hello there!

we have the function f(x) = IxI/x

let's analyze it:

when x is a positive number, suppose x = a, where a is positive, we have:

f(a) = IaI/a = a/a = 1

and this is independent of the number a, so for all the positive values of x, we have f(x) = 1

Now if x is negative, suppose x = -a, we have:

f(-a) = I-aI/(-a) = a/(-a) = -1

and again, this does not depend on the value of a, so for all the negative values of x, we have f(x) = -1.

And in x = 0 we have a little discontinuity, where f(0) is indefined.

Then this function can be piecewise writen as:

f(x) = 1 if x > 0

f(x) = -1 if x < 0