SOLUTION: What is the domain for y=15x/5x+10

Algebra ->  Algebra  -> Functions -> SOLUTION: What is the domain for y=15x/5x+10      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 104168: What is the domain for y=15x/5x+10
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!

y=%2815x%29%2F%285x%2B10%29 Start with the given function


5x%2B10=0 Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of x that make the denominator zero, then we must exclude them from the domain.



5x=0-10Subtract 10 from both sides


5x=-10 Combine like terms on the right side


x=%28-10%29%2F%285%29 Divide both sides by 5 to isolate x



x=-2 Divide

--------------------------------------------------------------
Answer:
So our answer is x=-2



Since x=-2 makes the denominator equal to zero, this means we must exclude x=-2 from our domain

So our domain is:

which in plain English reads: x is the set of all real numbers except x%3C%3E-2

So our domain looks like this in interval notation


note: remember, the parenthesis excludes -2 from the domain

If we wanted to graph the domain on a number line, we would get:

drawing%28500%2C50%2C-10%2C10%2C-10%2C10%2C%0D%0Anumber_line%28+500%2C+-12%2C+8%29%2C%0D%0Ablue%28arrow%280.2%2C-7%2C10%2C-7%29%29%2C%0D%0Ablue%28arrow%280.2%2C-6.5%2C10%2C-6.5%29%29%2C%0D%0Ablue%28arrow%280.2%2C-6%2C10%2C-6%29%29%2C%0D%0Ablue%28arrow%280.2%2C-5.5%2C10%2C-5.5%29%29%2C%0D%0Ablue%28arrow%280.2%2C-5%2C10%2C-5%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-7%2C-10%2C-7%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-6.5%2C-10%2C-6.5%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-6%2C-10%2C-6%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-5.5%2C-10%2C-5.5%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-5%2C-10%2C-5%29%29%2C%0D%0A%0D%0Acircle%280%2C-5.8%2C0.35%29%2C%0D%0Acircle%280%2C-5.8%2C0.4%29%2C%0D%0Acircle%280%2C-5.8%2C0.45%29%2C%0D%0Acircle%280%2C-5.8%2C0.4%29%2C%0D%0Acircle%280%2C-5.8%2C0.45%29%0D%0A%29 Graph of the domain in blue and the excluded value represented by open circle

Notice we have a continuous line until we get to the hole at x=-2 (which is represented by the open circle).
This graphically represents our domain in which x can be any number except x cannot equal -2