How do you find the vertical, horizontal or slant asymptotes for #h(x) = (2x - 1)/ (6 - x)#?

Answer 1

vertical asymptote x = 6
horizontal asymptote y = -2

Vertical asymptotes occur as the denominator of a rational function tends to zero. To find the equation let the denominator equal zero.

solve : 6 - x = 0 → x = 6 is the equation

Horizontal asymptotes occur as #lim_(x→±∞) f(x) → 0#

If the degree of the numerator and denominator are equal , as they are in this case , both degree 1 . The equation can be found by taking the ratio of leading coefficients.

# y = 2/-1 = -2 rArr y = -2 " is the equation "#

Here is the graph of the function. graph{(2x-1)/(6-x) [-10, 10, -5, 5]}

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Answer 2

To find the vertical asymptotes of ( h(x) = \frac{2x - 1}{6 - x} ):

Set the denominator equal to zero and solve for ( x ):

[ 6 - x = 0 ] [ x = 6 ]

So, ( x = 6 ) is a vertical asymptote.

To find the horizontal asymptote:

Compare the degrees of the numerator and the denominator:

The degree of the numerator is 1, and the degree of the denominator is also 1.

The horizontal asymptote is given by the ratio of the leading coefficients:

[ y = \frac{2}{-1} ] [ y = -2 ]

So, ( y = -2 ) is the horizontal asymptote.

To check for a slant (oblique) asymptote:

If the degree of the numerator is one more than the degree of the denominator, then there is a slant asymptote.

Here, the degree of the numerator is 1, and the degree of the denominator is also 1. Therefore, there is no slant asymptote for this function.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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