Question

how do i graph y= l2x-1l
The lines are absolute values

Answer 1

One way is to make a table of xy values

if x = 0, then
y = |2x-1|
y = |2*0-1|
y = |0-1|
y = |-1|
y = 1

Answer 2

if x = 1, then

y = |2x-1|
y = |2*1-1|
y = |2-1|
y = |1|
y = 1

Answer 3

if x = 2, then

y = |2x-1|
y = |2*2-1|
y = |4-1|
y = |3|
y = 3

Answer 4

if x = 3, then

y = |2x-1|
y = |2*3-1|
y = |6-1|
y = |5|
y = 5

Answer 5

do that with a few more x values to get more points. Then plot all of the points on the xy plane and draw a curve through them

Answer 6

Thank you very much. Do you know how I would figure out the domain and range?

Answer 7

what does the graph look like

Answer 8

you can use this to check

https://www.desmos.com/calculator

Answer 9

It looks like a v but i was always confused about the domain and range.

Answer 10

you should get this

https://www.desmos.com/calculator/tvfodpa7lf

Answer 11

are there any restricted x values?

Answer 12

ie are there any x values that lead to division by zero errors? or things like that?

Answer 13

i dont think so

Answer 14

because there are no restrictions, this means the domain is the set of all real numbers

Answer 15

you can plug in any real number you want, and some result will pop out for y

Answer 16

so thats the domain? How do i figure out range?

Answer 17

notice how on the graph, the graph stretches infinitely to the left and right along the x axis

Answer 18

as for the range, look for the lowest point. What is that lowest point?

Answer 19

(.5,0)?

Answer 20

yes, that's the vertex

notice the y coordinate of this point is y = 0

this is the lowest the graph goes. So the range is \(\Large y \ge 0\)

y can be any number as long as it's greater than or equal to 0