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

Dec 4, 2017

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

#### Explanation:

finding the point when y=0

$- \frac{1}{4} x - 1 = 0$

then $x = - 4$

when $x \le - 4$

$\left\mid - \frac{1}{4} x - 1 \right\mid = - \frac{1}{4} x - 1$

when $x > - 4$

$\left\mid - \frac{1}{4} x - 1 \right\mid = \frac{1}{4} x + 1$

both lines 'll be draw

$y = - \frac{1}{4} x - 1$

finding y-intercept when x=0

$y = - 1$ then the point to ubicate $\left(0 , - 1\right)$

when y=0
$x = - 4$ the point is $\left(- 4 , 0\right)$

for $y = \frac{1}{4} x + 1$

y-intercept is when x=0
$y = 1$ $\left(0 , 1\right)$

x-intercept is when y=0
$x = - 4$ $\left(- 4 , 0\right)$

Dec 4, 2017

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).
${f}_{1} : y = - \frac{1}{4} x - 1$ for $x \ge 0$
${f}_{2} : y = \frac{1}{4} x + 1$ for $x < 0$
Hope it helps