Complete the table of values for $f(x)=\frac{x^2+4x-5}{x-1}$.   

1. Graph the points in the table. What kind of function does it appear to be? Why is it not correct to connect all of the dots?

   Hint (a):

   Notice that there is no point at $x = 1$.

2. Look for a pattern in the values in the table. What appears to be the relationship between $x$ and $f\left(x\right)$? Calculate $f\left(0.9\right)$ and $f\left(1.1\right)$ and add the points to your graph. Is there an asymptote at $x = 1$? If you are unsure, calculate $f\left(0.99\right)$ and $f\left(1.01\right)$ as well.

   Partial Answer (b):

   The relationship between $x$ and $y$ appears to be linear. f$\left(0.9\right) = 5.9, f\left(1.1\right) = 6.1$.
   Although the line is approaching the point $\left(1, 6\right)$ from both sides, a point is not an asymptote.

3. Simplify the expression for $f\left(x\right)$. What do you think the complete graph looks like?

   Partial Answer (c):

   $f(x) = \frac{(x + 5)(x - 1)}{x - 1} = x + 5$

   Use the eTool below to complete the table.
   Click the link at right for the full version of the eTool: INT3 12-40 HW eTool