Equations involving modulus function

• Mar 5th 2013, 11:30 PM
Vishak
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.
• Mar 6th 2013, 12:33 AM
chiro
Re: Equations involving modulus function
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).
• Mar 6th 2013, 01:29 AM
Vishak
Re: Equations involving modulus function
Thanks heaps, I think I get it now. Do you know number 2?
• Mar 6th 2013, 03:51 PM
chiro
Re: Equations involving modulus function
Try doing the exact same thing and divide the graph when x < 1, x > 1, x < 3 and x > 3.
• Mar 6th 2013, 04:24 PM
Plato
Re: Equations involving modulus function
Quote:

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.