Absolute Value Sketching (1 Viewer)

[monkey187]

Hey I was wondering how I would go about sketching this graph

y = |2x - 1| + |x - 2|

thanks

 

[withoutaface]

you sketch one, sketch the other, then add a couple of points to find minima and gradients

 

[Slidey]

For this one, no x-intercepts exist.

 

[wogboy]

Locate the corners of the graph, which are at x=2 and x=1/2. (i.e. where the stuff inside the absolute value signs are zero), then:

For x >= 2,
y = (2x - 1) + (x - 2)
= 3x - 3

For 1/2 <= x < 2
y = 2x - 1 - (x - 2)
= x + 1

For x < 1/2
y = - (2x - 1) - (x - 2)
= - 3x + 3

Should be straightforward to graph now.

 

[t-i-m-m-y]

sketch the two separate graphs and add graphically