How do you graph $y = \frac{4}{x - 6} + 19$ $y=4/(x-6)+19$ using asymptotes, intercepts, end behavior?

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How do you graph $y = \frac{4}{x - 6} + 19$ $y=4/(x-6)+19$ using asymptotes, intercepts, end behavior?

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Answer 1 · 2016-11-13T04:58:43

Please read the reference and the explanation.

Explanation:

Multiply both sides by $x - 6$ $x - 6$ :

$x y - 6 y = 4 + 19 x - 114$ $xy - 6y = 4 + 19x - 114$

$x y - 6 y = 19 x - 110$ $xy - 6y = 19x - 110$

This is a rotated Hyperbola.

Here is a helpful Reference

Arrange in accordance with the quadratic equation in the reference:

$x y - 6 y - 19 x - 110 = 0$ $xy - 6y - 19x - 110 = 0$

Here are the values of their coefficients:

$A_{x y} = \frac{1}{2}, B_{x} = - \frac{19}{2}, B_{y} = - 3, C = - 110, and A_{xx} = A_{y y} = 0$ $A_(xy) = 1/2, B_x = -19/2, B_y = -3, C = -110, and A_("xx") = A_(yy) = 0$

Find the center:

$D = | (A_("xx"), A_(xy)), (A_(xy),A_(yy)) | = | (0,1/2), (1/2,0) | = -1/4$

$x_c = -1/D | (B_x, A_(xy)), (B_y,A_(yy)) | = 4| (-19/2, 1/2), (-3,0) | = 4(3/2) = 6$

$y_c = -1/D | (A_("xx"), B_x), (A_(xy),B_y) | = 4| (0, -19/2), (1/2,-3) | = 4(19/4) = 19$

The center is $(6,19)$

The calculation for the vertices is very long so I will just give them to you $(4,17)$ and $(8,21)$

Here is a graph:

![Desmos.com]( useruploads.socratic.org )

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How do you graph $y = \frac{4}{x - 6} + 19$ $y=4/(x-6)+19$ using asymptotes, intercepts, end behavior?

1 Answer

Explanation:

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How do you graph y=4/(x-6)+19y=4x−6+19y=4/(x-6)+19 using asymptotes, intercepts, end behavior?

1 Answer

Explanation:

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How do you graph $y = \frac{4}{x - 6} + 19$ $y=4/(x-6)+19$ using asymptotes, intercepts, end behavior?