Question

How do you graph y=(2|x-1|)/x-1?

Answer 1

Use graphing calculator.

Answer 2

I know the answer, but I need to know how to graph it myself.

Answer 3

just do it the old fashioned way
plug in some values for x and work out the y value
x = -5,-4,-3,-2,-1,0,1,2,3,4,5

Answer 4

Is there a reason why the graph doesn't look like a v, even with absolute value in the equation?

Answer 5

because we are dividing by x-1

Answer 6

HI!!

Answer 7

don't be fooled by this, it is just two horizontal lines

Answer 8

\(|x-1|=1-x\) if \(x<1\) or \(x-1\) if \(x>1\)

Answer 9

\[y = 2\left| x-1 \right|\]
this would give us a V shaped graph

Answer 10

so all you really have is \(-2\) if \(x<1\) or \(2\) if \(x>1\)

Answer 11

So the y is constant, and it's not in the shape of a v because we are dividing by x-1?

Answer 12

\[\frac{2(x-1)}{x-1}=2\\
\frac{2(1-x)}{x-1}=-2\]

Answer 13

in other words, this is a rather silly way of just saying \[f(x) = \left\{\begin{array}{rcc}
-2& \text{if} & x <1 \\
2& \text{if} & x >1
\end{array}
\right.
\]