How do you graph, find the zeros, intercepts, domain and range of f(x)=1/3abs(2x-1)?

1 Answer
Feb 20, 2018

domain {x, x in(-oo,+oo)}
range color(white)("d") {y, y in[0,+oo)}

See explanation.

Explanation:

This is of graph type vv.

The part |2x-1| is always positive so 1/3|2x-1| is also always
positive. Thus y>=0

color(blue)("Determin the vertex")

Set y=0=1/3|2x-1|

Multiply both sides by 3/1

y=0=|2x-1|

y=0=|0|

So 2x-1=0=>x=1/2

So the the vertex of vv is at (x,y)->(1/2,0)

Thus the vertex is on the x-axis. There is no plot below the x-axis.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Determine the y-intercept")

Set x=0 giving:

y=1/3|0-1|

y=1/3xx(+1) = 1/3

y_("intercept")->(x,y)=(0,1/3)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Plot two graphs but cit them off so that there is no line below the x-axis

Line 1 y=1/3(2x-1) where x<=0
Line 2 y=1/3(2x-1) where x>=0

Tony BTony B