Thread: Equations involving modulus function

Hi, I've been given homework problems from topics that I haven't been taught yet, and I have no idea how to start them, can't find any information in my textbooks Could somebody please explain to me how to go about these problems. They're both similar.

1) Graph the equation |x| + |y| = 1. Explain whether the graph represents the graph of a
function of x.

2) Given f(x) =|x - 1| - |x - 3|
(a) Draw the graph of f(x).
(b) Determine the domain and range of f(x).
(c) Use your graph to solve the inequality |x - 1| - |x - 3| >= 5

Thanks heaps.

Hey Vishak.

I'll start you off with a hint: For Q1 consider |x| = x if > 0 and -x if < 0 and same for y. You will have four different functions to graph and you can graph them all that fit the criteria.

Just to be specific, one example is x + y = 1 where x > 0 and y > 0 (both positive).

Thanks heaps, I think I get it now. Do you know number 2?

Try doing the exact same thing and divide the graph when x < 1, x > 1, x < 3 and x > 3.

Originally Posted by Vishak

Hi, I've been given homework problems from topics that I haven't been taught yet, and I have no idea how to start them, can't find any information in my textbooks Could somebody please explain to me how to go about these problems. They're both similar.
1) Graph the equation |x| + |y| = 1. Explain whether the graph represents the graph of a
function of x

Have you actually done any web searches? Look at this.