Respuesta :
Answer:
(B) The correct answer is B: m = n, so y = am / bn is the horizontal asymptote.
The second part is The horizontal asymptote is y = 5
The horizontal asymptote is a horizontal line that guides the graph for values of x, but is not part of the graph
The correct option that defines the horizontal asymptote is the option;
- m = n, so the horizontal asymptote is [tex]\underline {y = \dfrac{a_m}{b_n}}[/tex]
Reason:
The possible function of the question is [tex]f(x) = \dfrac{20 + 5 \cdot x}{x}[/tex]
The general form of the rational function is presented as follows;
[tex]f(x) = \dfrac{x^m+...+ a \cdot x + c}{x^n + ...+b\cdot x + d}[/tex]
The power or degree of the numerator and denominator of a rational function determine the nature of the horizontal asymptote
Where highest power in numerator is less than the highest power or degree of the denominator, the horizontal asymptote is at y = 0
Therefore;
m < n the horizontal asymptote is y = 0
Where the power of the numerator is larger than the power of the denominator by one, the asymptote is slant, and the graph has no asymptote
m > n, there is no horizontal asymptote
In a rational function where the power of the numerator is equal to the power of the denominator, the horizontal asymptote occurs at the ratio of the leading zeros, [tex]y = \dfrac{a_m}{b_n}[/tex]
m = n, the horizontal asymptote is [tex]y = \dfrac{a_m}{b_n}[/tex]
Therefore;
In the given function, [tex]f(x) = \dfrac{20 + 5 \cdot x}{x}[/tex], the power of the numerator is equal to the power of the denominator, therefore, we have;
- m = n, so the horizontal asymptote is [tex]\underline {y = \dfrac{a_m}{b_n}}[/tex]
The horizontal asymptote of the function is [tex]y = \dfrac{5}{1} = 5[/tex]
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https://brainly.com/question/12730051
