Question

How do you graph `y = | -1/4x -1|`?

Answer 1

graph{abs(-1/4x-1) [-10, 10, -5, 5]}

Explanation:

finding the point when y=0

`-1/4x-1=0`

then `x=-4`

when `x<=-4`

`abs(-1/4x-1)=-1/4x-1`

when `x> -4`

`abs(-1/4x-1)=1/4x+1`

both lines 'll be draw

`y=-1/4x-1`

finding y-intercept when x=0

`y=-1` then the point to ubicate `(0,-1)`

when y=0
`x=-4` the point is `(-4,0)`

for `y=1/4x+1`

y-intercept is when x=0
`y=1` `(0,1)`

x-intercept is when y=0
`x=-4` `(-4,0)`

Answer 2

if x=0 then y=1
if x=-4 then y=0
if x=-8 then y=1 (as well)

Explanation:

Absolute value mirrors everything that is in negative numbers to the positive numbers.
I simply draw a net. Then put instead of x a number. For example:
x=0 then y=1
if x=-4 the y=0
Now you can draw a line that goes through this two points. The other part will be mirrored just like the right side. Let's see.
Let's put instead of x a number -8. Then y=1 just as for the x=0.
Hope it helps.
There is also a way to split this function into two(a bit useless for this particular example).
`f_1: y=-1/4x-1` for `x>=0`
`f_2: y=1/4x+1` for `x<0`
Hope it helps