CPM Homework Help : CALC Problem 1-171

Write a complete set of approach statements for $y = \frac { ( 2 x + 1 ) ( 2 - x ) } { 2 x + 1 }$ .

Hint:

Other than $±∞$ , what other $x$ value(s) are approached but never reached? Consider when the function's $y$ -value is undefined.

More Help:

Remember that a value can be approached from both the positive and negative side.

Answer:

$\text{As }x\rightarrow -\infty ,\ y\rightarrow \infty .$

$\text{As }x\rightarrow \infty ,\ y\rightarrow -\infty .$

$\text{As }x\rightarrow -\frac{1}{2}^{-} ,\ y\rightarrow \frac{5}{2} .$

$\text{As }x\rightarrow -\frac{1}{2}^+ ,\ y\rightarrow \frac{5}{2} .$