SOLUTION: Hello again my friends. Can someone help me solve this problem ? Also I would like to know if anyone can Direct me to a place to get more Examples that look like this problem ? I c

Algebra ->  Absolute-value -> SOLUTION: Hello again my friends. Can someone help me solve this problem ? Also I would like to know if anyone can Direct me to a place to get more Examples that look like this problem ? I c      Log On


   

Question 950955: Hello again my friends. Can someone help me solve this problem ? Also I would like to know if anyone can Direct me to a place to get more Examples that look like this problem ? I can not find any examples anywhere that have solutions or problems that look like this . This is an absolute value problem . The question asks us to graph the function and to find the domain. Thank you and I appreciate the Help!!
F(t)= |t+2|/t+2
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
F has two critical values. Undefined for t=0, and change in sign of the absolute value at t=-2. These values form three intervals on t.

t%3C-2:
F%28t%29=abs%28t%2B2%29%2Ft%2B2
F%28t%29=-%28t%2B2%29%2Ft%2B2
F%28t%29=%282-t%29%2Ft%2B2t%2Ft
F%28t%29=%282-t%2B2t%29%2Ft
F%28t%29=%28t%2B2%29%2Ft
No vertical nor horizontal asymptotes nor roots in this interval.
This IS a slant asymptote. F%28t%29=1%2B2%2Ft, so as t goes unbound to the left, F approaches the line y=1. You can pick a few other values in the interval to help in finding the graph or shape.

AT t=-2:
abs%280%29%2F%28-2%29%2B2=2
The sharp corner point is (-2,2).

t%3E=-2:
Mostly about the greater-than part,
F=%28t%2B2%29%2Ft%2B2
F=%28%28t%2B2%29%2B2t%29%2Ft
F=%283t%2B2%29%2Ft
Root at -2%2F3 DOES occur in this interval.
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Consider what happens to the left of t=0 and to the right of t=0, and decide the behavior arount t=0. Remember, F has NO value at t=0.

graph%28300%2C300%2C-5%2C5%2C-3%2C7%2Cabs%28x%2B2%29%2Fx%2B2%29