Question

Graph the following function using transformations. Find the vertical and horizontal asymptotes. State the domain and range.
f(x) = 5+ 1/x+4. Please show work. @Calculus1

Answer 1

i advice u to use wolfralpha

Answer 2

is this like this?
f(x) = 5+ 1/(x+4)

Answer 3

MArk o...it doesnt show parenthesis around...

Answer 4

http://www.wolframalpha.com/input/?i=f%28x%29+%3D+5%2B+1%2F%28x%2B4%29

Answer 5

so, is:
\[f(x)=5+\frac{1}{x}+4\]
correct? or is mark's interpretation correct:
\[f(x)=5+\frac{1}{x+4}\]
?

Answer 6

the second one...agreene...

Answer 7

Okies.
For the vertical asymptotes, you need to find areas where the function wont be defined. in this case where null division happens.
x+4=0
x=-4
So, we have a vertical asymptote at x=-4
For the horizontal, we then look to the highest powers of x, and ignore everything else giving us: \[\frac{1}{x}\]
we then take away the x's giving us our horizontal asymptote: \[\frac{0}{1}=0\]
So, our asymptotic regions are:
x=-4 (Vertical) and x=0 (Horizontal)
As for domain and range, there are no restricting agents in the function, causing
\[-\infty\le x\le \infty\]
\[-\infty \le y \le \infty\]

Answer 8

Thank you agreene!

Answer 9

agreene- so what would the graph look like then??