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Functions

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(a)Consider the function:
f(x)=(7x+13)/(13x-1)
(i)Calculate the exact values of the coordinates of the points of intersection of the graph of this function with the coordinate axes.
(ii)Calculate the equations of the asymptotes

(b)The line h(x)=ax+b passes through (-1,-3) and (3,5).
(i)Calculate a and b.
(ii)Solve f(x)<h(x)

help!!!

  • Functions - ,

    (a) The function intersects the x axis where f(x) = y = 0. That would be where x = -13/7. It intersects the y axis where x = 0. At that point, the function tells you that y = -13.

    There is a vertical asymptote there the denomiator is zero. (x = 1/13). As approaches infinity, f(x) approaces y = 7/13. That is a horizontal asymptote.

    (b) Solve ths pair of equations for a and b:
    -3 = -a + b
    5 = 3a + b

    The first step should tell you that a = 2. b = -1 h(x) = 2x -1

    Once you have h(x), solve the inequality
    (7x + 13)/(13 x-1) < 2x -1

    I'll leave that step up to you

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