Question

sketch the graph of 1/(x+1) + 1/(x-1) by finding the horizontal and vertical asymptotes and also find critical points and inflection points. ​

Answer 1

Answer:

The function is defined for all

x

except the points

x

=

±

1

where it has discontinuities.

The function has no roots

(

x

−

intercepts. Calculate the

y

−

intercept:

x

=

0

,

⇒

f

(

0

)

=

1

1

−

0

2

=

1.

We see that the function is positive for

x

∈

(

−

1

,

1

)

and negative for

(

−

∞

,

−

1

)

∪

(

1

,

∞

)

.

The function is even since

f

(

−

x

)

=

1

1

−

(

−

x

)

2

=

1

1

−

x

2

=

f

(

x

)

.