SOLUTION: i have to graph an open sentence its for absolute value. i know that if i have /x/=3 this is is x=3 or x=-3 but how do i graph y=2/x+4/ its y=2x+4 or ???

Algebra ->  Absolute-value -> SOLUTION: i have to graph an open sentence its for absolute value. i know that if i have /x/=3 this is is x=3 or x=-3 but how do i graph y=2/x+4/ its y=2x+4 or ???      Log On


   

Question 729979: i have to graph an open sentence its for absolute value. i know that if i have /x/=3 this is is x=3 or x=-3 but how do i graph y=2/x+4/ its y=2x+4 or ???
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The variable expression, x+4, may be either positive or negative, depending on the value of x.

When x%2B4%3E=0, y=2abs%28x%2B4%29 is y=2%28x%2B4%29 or y=2x%2B8. You must restrict the graph of this line to satisfy x%2B4%3E0 which is x%3E=-4.

When x%2B4%3C0, y=2abs%28x%2B4%29 is y=2%2A%28-1%29%28x%2B4%29, or y=2%28-x-4%29, or y=-2x-8. You must restrict the graph of this line to satisfy x%2B4%3C0 which is x%3C-4.

IN CASE OF CONTINUED DIFFICULTY:
The absolute value of an expression requires simple but careful attention to logic. |x+4| will always be positive or zero. NEVER Negative.
If x+4=0>0, then |x+4|=x+4.
If x+4<0, then |x+4|=-(x+4)=-x-4.
Really that is based on the meaning of absolute value.
For any variable, v, we can consider how far is v from zero on the number line. |v| is the distance from zero on the number line. v is a variable, so by itself, we do not know its value; but |v| is equal to v if v%3E=0, and |v| is equal to -v if v%3C0.
Drawing a number line makes this easier to SEE.