The graph of R intersects with the horizontal or oblique asymptote at (-3, 0)
The horizontal asymptote
The function is given as:
[tex]R(x)=\frac{x+3}{x\left(x+8\right)}[/tex]
Set the numerator to 0
[tex]R(x)=\frac{0}{x\left(x+8\right)}[/tex]
Evaluate
R(x) = 0
This means that the horizontal asymptote of R(x) is y = 0
The oblique asymptote
The function is given as:
[tex]R(x)=\frac{x+3}{x\left(x+8\right)}[/tex]
The numerator has a degree of 1, while the denominator has a degree of 2
When the degree of the numerator is less than the degree of denominator, then the function has no oblique asymptote
Hence, the function has no oblique asymptote.
Intersection of the function and the horizontal asymptote
In (a), we have:
R(x) = 0
Substitute R(x) = 0 in [tex]R(x)=\frac{x+3}{x\left(x+8\right)}[/tex]
[tex]\frac{x+3}{x\left(x+8\right)} = 0[/tex]
Cross multiply
x + 3 = 0
Solve for x
x = -3
So, we have:
(x, y) = (-3, 0)
Hence, the graph of R intersects with the horizontal or oblique asymptote at (-3, 0)
Read more about asymptotes at:
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