$\"\"$

The function is $\"\"$ .

The denominator is zero when x = 1.

So, the domain of f is all real numbers except x = 1.

To determine the behavior of f near this excluded value, evaluate f(x) to the left and right of x = 1. $\"\"$

The domain of f is all real numbers except x = 1.

$\"\"$

The function is $\"\"$ .

Make the table : 1

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

\ x \	\ $\"\"$ \
\ 0.5 \	\ $\"\"$ \
\ 0.9 \	\ $\"\"$ \
\ 0.99 \	\ $\"\"$ \
\ 0.999 \	\ $\"\"$ \

$\"\"$

Make the table : 2

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

\ x \	\ $\"\"$ \
\ 1.5 \	\ $\"\"$ \
\ 1.1 \	\ $\"\"$ \
\ 1.01 \	\ $\"\"$ \
\ 1.001 \	\ $\"\"$ \

$\"\"$

Make the table : 3

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

\ x \	\ $\"\"$ \
\ $\"\"$ \	\ $\"\"$ \
\ $\"\"$ \	\ $\"\"$ \
\ $\"\"$ \	\ $\"\"$ \
\ $\"\"$ \	\ $\"\"$ \

$\"\"$

Make the table : 4

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

\ x \	\ $\"\"$ \
\ $\"\"$ \	\ $\"\"$ \
\ $\"\"$ \	\ $\"\"$ \
\ $\"\"$ \	\ $\"\"$ \
\ $\"\"$ \	\ $\"\"$ \

$\"\"$

The function is $\"\"$ .

The denominator is zero when x = 1.

So, the domain of f is all real numbers except x = 1.

To determine the behavior of f near this excluded value, evaluate f(x) to the left and right of x = 1.

Obsrve the tables x approaches 1 from the left, f(x) decreases without bound. In contrast, as x approaches 1 from the right, f(x) increase without bound. $\"\"$

The behavior of f near x = 1 is $\"\"$ .