Question

y=2/x-3+1 (i already graphed it)
http://mathway.com/answer.aspx?p=grap?p=ySMB012SMB10x-3+1?p=False?p=False?p=True?p=False?p=True?p=-10?p=10?p=-10?p=10

Answer these questions using your graph:
a. What is the domain?
b. What is the range?
c. Name the vertical asymptotes, if any
d. Name the horizontal asymptotes, if any
e. Name the zeros, if any

Answer 1

i think you graphed it incorrectly

Answer 2

i assume it is \(y=\frac{2}{x-3}+1\)

Answer 3

mhmm can you fix it for me and help me out ?

Answer 4

you graphed \(y=\frac{2}{x}-3+1=\frac{2}{x}-2\)

Answer 5

you need parentheses for the denominator
try here
http://mathway.com/answer.aspx?p=grap?p=ySMB012SMB10%28x-3%29+1?p=False?p=False?p=True?p=False?p=True

Answer 6

i hope you see the difference. be careful when you input fractions
can you answer the questions now or still confusing?

Answer 7

im still confused ... like really bad haha

Answer 8

ok lets look at the picture i sent

Answer 9

we start with the domain first
since you cannot divide by 0 you have to make sure that \(x-3\neq 0\) which means \(x\neq 3\)

Answer 10

therefore the domain is all real numbers except \(x=3\)
now to the vertical asymptote, which is essentially answered by the first part
you see from the picture that the function approaches the vertical line \(x=3\) but does not cross it. that is the vertical asymptote

Answer 11

you should see that from the graph
now to the horizontal asymptote
from the picture, you see that the graph approaches the horizontal line \(y=1\)
that is, to the right on the graph and to the left on the graph the curve is getting closer to \(y=1\) and that is your horizontal asymptote

Answer 12

we would have know this without the graph, because for \(y=\frac{2}{x-3}+1\) as \(x\) gets larger \(\frac{2}{x-3}\) gets close to zero, so the whole thing gets close to 1

Answer 13

this also answers the question about the range
since the range is all possible \(y\) values, and since the curve gets close to 1 but is never equal to 1, the range is all real numbers except \(y=1\)