Using a calculator to build a table and a graph or using a graphing calculator, describe the behavior of the graph of the equation as x approaches 8. $$y = - \frac { x + 8 } { ( x + 1 ) ( x - 8 ) }$$
A) Y approaches $- 1$ from the left and $1$ from the right.
B) Y approaches $- \infty$ from the left and $+ \infty$ from the right.
C) Y approaches $+ \infty$ from the left and $- \infty$ from the right.
D) Y approaches $1$ from the left and $- 1$ from the right.
E) Y approaches 8.

Question

Quizplus · Accepted Answer

As $x$ approaches 8, the denominator of the fraction $(x + 1)(x - 8)$ approaches 0, causing the value of $y$ to approach infinity. However, because the denominator changes sign at $x = 8$ (from positive to negative as $x$ increases through 8), $y$ will approach $+ \infty$ from the left of 8 and $- \infty$ from the right of 8. This is due to the negative sign in front of the fraction, which inverts the direction of the approach.

Using a Calculator to Build a Table and a Graph y=−x+8(x+1)(x−8)y = - \frac { x + 8 } { ( x + 1 ) ( x - 8 ) }y=−(x+1)(x−8)x+8​

Using a Calculator to Build a Table and a Graph $y = - \frac { x + 8 } { ( x + 1 ) ( x - 8 ) }$