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2021-02-25

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

Neelam Wainwright

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

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

Explanation:
In mathematics, a rational function is defined as the ratio of two polynomial functions. The general form of a rational function is:
$f\left(x\right)=\frac{P\left(x\right)}{Q\left(x\right)}$ where $P\left(x\right)$ and $Q\left(x\right)$ 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 $P\left(x\right)$ is greater than or equal to the degree of the denominator polynomial $Q\left(x\right)$, 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 $P\left(x\right)$ is less than the degree of $Q\left(x\right)$, 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

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:
$f\left(x\right)=\frac{P\left(x\right)}{Q\left(x\right)}$ where $P\left(x\right)$ and $Q\left(x\right)$ are polynomials.
In the graph of a rational function, the vertical asymptotes occur where the denominator $Q\left(x\right)$ 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.
$\overline{)\text{True}}$

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