Posted by **karthi** on Wednesday, November 27, 2013 at 1:01pm.

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 -
**Steve**, Wednesday, November 27, 2013 at 3:57pm
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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