True or False. The graph of a rational function may intersect a horizontal asymptote.

allhvasstH

allhvasstH

Answered question

2021-02-25

True or False. The graph of a rational operate could encounter a horizontal straight line.

Answer & Explanation

Neelam Wainwright

Neelam Wainwright

Skilled2021-02-26Added 102 answers

1:
True, the graph of a rational function can cross a horizontal Asymptote.
2:
Its
madeleinejames20

madeleinejames20

Skilled2023-05-29Added 165 answers

The graph of a rational function could encounter a horizontal straight line' can be represented as:
True or False. The graph of a rational function could encounter a horizontal straight line?
To answer this statement, we can say:
False. The graph of a rational function cannot encounter a horizontal straight line.
Eliza Beth13

Eliza Beth13

Skilled2023-05-29Added 130 answers

Answer: False
Explanation:
In mathematics, a rational function is defined as the ratio of two polynomial functions. The general form of a rational function is:
f(x)=P(x)Q(x) where P(x) and Q(x) are polynomials.
Now, to determine whether the graph of a rational function can intersect a horizontal straight line, we need to consider the behavior of the function as x approaches positive or negative infinity.
If the degree of the numerator polynomial P(x) is greater than or equal to the degree of the denominator polynomial Q(x), then the graph of the rational function may have a horizontal asymptote. In this case, the function approaches a constant value as x goes to infinity or negative infinity.
If the degree of P(x) is less than the degree of Q(x), then the rational function may have a slant asymptote. The function approaches a linear function as x approaches infinity or negative infinity.
In either case, since the function approaches a certain value or a linear function as x becomes extremely large or small, the graph of a rational function cannot intersect a horizontal straight line. The function either approaches the horizontal line or diverges away from it.
Therefore, the statement 'The graph of a rational function could encounter a horizontal straight line' is false.
Mr Solver

Mr Solver

Skilled2023-05-29Added 147 answers

True or False. The graph of a rational function could intersect a horizontal straight line.
To determine whether this statement is true or false, we need to consider the characteristics of rational functions.
A rational function is defined as the ratio of two polynomial functions, where the denominator is not equal to zero. The general form of a rational function is given by:
f(x)=P(x)Q(x) where P(x) and Q(x) are polynomials.
In the graph of a rational function, the vertical asymptotes occur where the denominator Q(x) is equal to zero. However, there are no restrictions on the horizontal behavior of the graph.
Therefore, it is true that the graph of a rational function could intersect a horizontal straight line.
True

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