# Function

Visitor
2016-08-09 08:43:21
#1
We have the function f:R{2} - > R, f(x) = (x + 4) / (2 - x)
Where the function intersects the axis Ox and Oy?
Where is the point of intersection between f graph and the line bisector y = x ?

## RE: Function, intersection with Ox Oy

TeacherM
Visitor
2016-08-09 09:09:06
#2
We have to solve these two equations:
f(x) = 0, and
y = f(0)

So, first
$f(x)=0 => \frac{x+4}{2-x} = 0 => x+4 = 0 => x = -4$
so though, (-4, 0) is the point where the graph meet the axis Ox.

and the second

$f(0)=\frac{0+4}{2-0} = 2$
so though, (0,2) is the point where the graph meet Oy axis

## RE: Function intersects the line y = x

Sammaritean
Visitor
2016-08-12 05:29:30
#3
For the intersection with the line y = x, we have to solve the equation f(x) = x. So though, we have
$\frac{x+4}{2-x} = x => x+4 = 2x - x^{2} => x^{2}-x+4=0$
Further, we have
$\Delta = 1 - 16 = -15 <0$
So though, the equation has no real solutions.
Finally, the f graph doesn't intersects the line y = x.