Respuesta :
points of discontinuity are x = √-2.
x = √-2 is non removable discontinuity.
The x- intercept is x = 0.
The y- intercept is y = 0.
How to find the points of discontinuity of the rational function & find the x - and y -intercepts of the rational function?
points of discontinuity:
In rational functions, points of discontinuity are defined as fractions with undefined or zero as their denominator. When the denominator of a fraction is 0, the fraction is no longer defined and shows up as a hole or break in the graph.
points of discontinuity removable:
A point on the graph that is removable discontinuity is one that may be filled in with a single value despite not existing.If an is zero for a factor in the denominator that shares a factor with a factor in the numerator, a removable discontinuity at x=a in the graph of a rational function occurs.
points of discontinuity non removable:
A function's break that cannot be repaired with a single point is referred to as a non-removable discontinuity. It cannot be filled in with a single point, a vertical asymptote (a vertical line that the graph approaches but never crosses because the function is undefined at that x-value) is non removable.
given that
[tex]y = \frac{x²+2x}{ x²+2}[/tex]
cancel the common factors.
[tex]y = x[/tex]
now,
points of discontinuity are
[tex] {x}^{2} + 2 = 0 \\ x = \sqrt{ - 2} [/tex]
Here x = √-2 is non removable discontinuity.
The x- intercept is
if x = 0, then
y = x
y = 0
The y- intercept is
if y = 0, then
0 = x
x = 0.
Learn more about rational functions from here:
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