Question

Please help

sketch the graph of the continuous function
f:R\{-1} -> R : x-> (x+1)(X-2)/(x+1).
justify your answer.

Answer 1

I don't understand what that says.

y = (x+1)(x-2)/(x+1) is discontinuous at x = -1 because of division by 0.

You can simplify that to:

\[y = (x-2) , \ x\neq -1\]
Just graph that line, and put an open circle at x = -1

Answer 2

when i differentiate the function i keep getting -1 as my root which i don't think is possible as you cannot divide by zero on the bottom. i'm really confused

Answer 3

\[y=(x-2)\]\[dy/dx=\frac{ (x+1)(x-2)-(x+1)(2x-1) }{ (x+1)^2}\]
\[\frac{ x+2 }{ (x+1) }=\frac{ 2x-1 }{ (x+1) }\]
\[x+1=2x-1\]
\[x=1\]
but this is not necessary no maxima required

Answer 4

I think you made a little error:

Answer 5

sorry

Answer 6

when i differentiate the function i keep getting -1 as my root

The roots of this "polynomial" are where it crosses the x-axis i.e. where y=0
(x+1)(X-2)/(x+1) =0
x=- 1 must be excluded because that would cause division by 0.
x=2 is a valid root.

If you differentiate and set that to zero you can find the min or max of the polynomial
in this case you find the differential is 1, a constant. That means no max or min.

Of course, if you first simplify by cancelling (x+1), you get
y= x-2
which is the equation of a line with slope 1 and y-intercept -2
that would be the plot, but with an excluded value at x= -1 to account for the division by (x+1) in the original expression.