  ### Home > INT3 > Chapter Ch12 > Lesson 12.1.3 > Problem12-40

12-40.

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

 $x$ $–2$ $–1$ $0$ $1$ $2$ $3$ $f\left(x\right)$

Doing the substitutions yourself will help you understand what is happening in this problem.

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?

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.

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?

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

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