A rational function of the form f(x) = (a/(x-1))+k, has a y-intercept of 4 and an x-intercept of 2. What is the value of "a" and "k"?

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  • Pope
    Lv 7
    3 years ago
    Favorite Answer

    The graph of y = f(x) has those given intercepts, not actually the function itself.

    The y-intercept is 4.

    f(0) = 4

    [a/(0 - 1)] + k = 4

    -a + k = 4

    The x-intercept is 2.

    f(2) = 0

    [a/(2 - 1)] + k = 0

    a + k = 0

    -a + k = 4

    a + k = 0 (+)

    -------------

    2k = 4

    k = 2

    a + 2 = 0

    a = -2

  • Mike G
    Lv 7
    3 years ago

    4 = -a + k

    0 = a + k

    a = -2

    k = 2

    See Graph

    https://www.desmos.com/calculator/tcrkhysvxb

  • alex
    Lv 7
    3 years ago

    y-intercept of 4 --->f(0)=4

    and

    x-intercept of 2 --->f(2)=0

    solve 2 equations for the values of a , k

  • david
    Lv 7
    3 years ago

    f(x) = (a/(x-1)) + k

    4 = (a/(0-1)) + k ... k = 4 + a

    0 = (a/(2-1)) + k ... k = -a <<< add both

    . . . . . . . . . . . . . 2k = 4 ... k = 2

    .... k = -a .... a = -2

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