Write the equation for the translation of y= 7/x that has asymptotes at x=-3 and y = 17

Question

Write the equation for the translation of y= 7/x that has asymptotes at x=-3 and y = 17

in progress 0
2022-04-19T17:04:39+00:00 2 Answers 0

Answers ( 2 )

  1. Violet
    0
    2022-04-19T17:06:00+00:00

    Translate 7/x to the left by 3 and up by 17 to get:

    y = 17 + 7/(x+3)

  2. Kylie97
    0
    2022-04-19T17:06:12+00:00

    Let us consider the given function [tex] y=frac{7}{x} [/tex],

    It has a vertical asymptote at x=0, because x=0 makes the denominator 0, which is not defined.

    To have the vertical asymptote at x= -3, the denominator has to be x-(-3), or x+3.

    So, the function [tex] y=frac{7}{x+3} [/tex] has vertical asymptote at x = -3.

    Since, the function [tex] y=frac{7}{x+3} [/tex] has a horizontal asymptote at y=0.

    So, to get the horizontal asymptote at y=17 we have to add 17 to the function.

    Therefore, the function [tex] y=frac{7}{x+3}+17 [/tex] has a vertical asymptote at x = -3 and a horizontal asymptote at y = 17.

    So, Equation after the translation is:

    [tex] y=frac{7}{x+3}+17 [/tex].

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