Consider the given function.
y=x^2+2x/x^2+ 2
Recall that division by zero is not defined. Therefore, the rational function is undefined where x^2+ 2=0.
ccc
x^2+ 2=0
⇕
x^2= -2
Notice that there is no real number that satisfies the equality x^2=-2.
This means that all real numbers are included in the domain.
Domain
All real numbers
Points of Discontinuity
If a real number a is not in the domain of a function, then the function has a point of discontinuity at x=a. Since the domain is all real numbers there are no points of discontinuity of our function.
Intercepts
The intercepts of a function are the points where the graph intersects the axes. Let's calculate the intercepts of the given function, if there are any.
x-intercepts
The x-intercepts of a function are the points where the graph intersects the x-axis. At these points, the value of the y-coordinate is zero. Therefore, to find the x-intercepts, we have to substitute 0 for y in the function rule and solve for x.
The y-intercept of a function is the point where the graph intersects the y-axis. At this point, the value of the x-coordinate is zero.
Therefore, to find the y-intercept, we have to substitute 0 for x in the function rule and solve for y.
