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math

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Consider the function f(x)= 3
------.
x^2-25
a) Determine any restrictions on x.
b) State the domain and range.
c) State equation(s) for the asymptote(s).
d) Determine any x- and y-intercepts.
e) Sketch a graph of the function.
f) Describe the behaviour of the function as x approaches -5 and 5.

someone please kindly do this for me please. i beg you, please do all these for me please....

  • math - ,

    f(x) is not defined when the denominator is zero. So,

    (a) x ≠ ±5
    (b) domain is all reals except ±5
    The denominator is minimum when x=0, so f(x) < -3/25 when -5<x<5
    For |x| > 5 f(x) > 0, so the range is
    (-∞,-3/25)∪(0,∞)
    (c) vertical: x=±5
    horizontal: y=0
    (d) x: none
    y: -3/25
    (e) see wolframalpha.com
    (f) x -> +∞ for |x| > 5
    x -> -∞ for |x| < 5

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