Question

h(x) = absolute value of (x-1) divided by (x+2).
How do I write this function as a piecewise function? What are the horizontal asymptotes?

Answer 1

What do you think it is first?

Answer 2

\[h(x)=\frac{|x-1|}{x+2}\] like that?

Answer 3

if that is it we can continue

Answer 4

yes!

Answer 5

ok we start with the definition of \(|x-1|\) which is
\[ |x-1| = \left\{\begin{array}{rcc}
-x+1 & \text{if} & x<1 \\
x-1& \text{if} & x\ge1
\end{array}
\right.\]

Answer 6

in more simple english it is itself if x - 1 is positive, and its opposite if x -1 is negative
now all we need is to divide by \(x+2\)

Answer 7

\[h(x) =\frac{|x-1|}{x+2}= \left\{\begin{array}{rcc}
\frac{1-x}{x+2}& \text{if} & x<1 \\
\frac{x+1}{x+2}& \text{if} & x\geq 1
\end{array}
\right.\]

Answer 8

horizontal asymptotes next ?

Answer 9

dont you mean to say (x-1)/(x+2) if x is greater than or equal to 1, and not (x+1) as the numerator?

Answer 10

and yes, horizontal asymptotes i need help with. How would I go about solving?