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shorty888
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F(x)= 6x^2-17x-3/3x+2, find horizontal asymptote
shorty888 said:F(x)= 6x^2-17x-3/3x+2, find horizontal asymptote
shorty888 said:F(x)= 6x^2-17x-3/3x+2, find horizontal asymptote
There is also a diagonal asymptote but a word from the OP will be required to find out if such asymptotes have been taught.SuperSonic4 said:Do you mean $f(x) = \frac{6x^2-17x-3}{3x+2}$
A horizontal asymptote is a line where a function approaches but doesn't quite reach there. An example is y=0 for f(x) = e^x
There are no horizontal asymptotes in your case, there is a vertical one where 3x+2 = 0 but no horizontal ones.
nb: Please take care with brackets, I've guessed at what you meant but that isn't the literal meaning of what you wrote which would be $F(x) = 6x^2-17x-x+2$
A horizontal asymptote is a straight line that a function approaches as the input values get larger and larger or smaller and smaller. It is represented by the equation y = c, where c is a constant.
To find the horizontal asymptote of a rational function, you need to compare the degrees of the numerator and denominator. If the degree of the numerator is smaller than the degree of the denominator, the horizontal asymptote is y = 0. If the degrees are the same, the horizontal asymptote is the ratio of the leading coefficients of the numerator and denominator. If the degree of the numerator is larger than the degree of the denominator, there is no horizontal asymptote.
No, a rational function can only have at most one horizontal asymptote. This is because the behavior of a rational function as the input values get larger or smaller is determined by the degrees of the numerator and denominator.
If the degrees of the numerator and denominator are the same, the horizontal asymptote is the ratio of the leading coefficients of the numerator and denominator. For example, if the rational function is f(x) = (2x + 3)/(4x + 5), the horizontal asymptote is y = 2/4 or y = 1/2.
No, the horizontal asymptote of a rational function never intersects the graph of the function. This is because, by definition, the horizontal asymptote is a line that the function approaches but never touches.