Question

Draw the graph of y=|x|+|x-2|

Answer 1

Answer:

Step-by-step explanation:

y=|x−1|+|x−2|  

So, equate both the linear expressions with 0. And the resulting value will be the intersection of the equation under modulus and the x-axis.

So, x−1=0 and x−2=0

∴x=+1and x=+2

And then plot this small figure, which defines the modulus function's sign before and after intersection.

And then, combine both of them to get a rough idea about the shape.

And, then break the modulus function into pieces.

y=⎧⎩⎨−(x−1)−(x−2)(x−1)−(x−2)(x−1)+(x−2)if x≤1if 1 < x<2if x≥2

And, on solving these, we get

y=⎧⎩⎨−2x+312x−3if x≤1if 1 < x<2if x≥2

If you're wondering why, i added those negative signs before few linear expressions.

Here's why i did so?

If you put any random values from the domain of 'x' written in the right hand side of the piecewise expansion of the function, and if you land up with a negative number, put a negative sign. Or if you get a positive number, leave it as it is just convert '∣’ into parenthesis.

And, you'd have to do this for each and every piece.

For example, lets consider the1stpart. Since, we have two modulus functions, we'll first consider|x−1|. Now, put any value from its domain. Like for example, i choose -3 (which is <−2 as per the domain ) and i get '-4′. So, it's negative. Hence, i added a negative sign before the brackets.

Do the same for each and every piece.

Now, graph these piece wise.

Since, all are linear, you'll find no difficulty. If you're new at graphing and you don't even know, how to graph this. Check this as a reference, Ankit Kumar Sharma's answer to Draw the graph of the linear equation x+2y=8?

And, then combining all of them, and graphing them in their domain only.

And, this is your graph.

Hope this helps!