# 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.

• 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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