Write an equation for each vertical asymptote ...

Question

http://imgur.com/5G22pte   <---link

For the function f whose graph is shown, give the value of each quantity, if it exists. If the limiting behavior is ∞ or −∞, so state. If the limit does not exist, write DNE.

lim x→−3 f(x) 

lim x→3 f(x)

lim x→−2 f(x)

Write an equation for each vertical asymptote of the curve y= f(x). 

Answer 1

Step 1:

Observe the graph of the function:

We can observe from the graph that  exists.

As tends to from the left hand side, tends to .

As tends to from the right hand side, tends to .

Since the left hand limit and right hand limit are equal,

Solution:

.

Answer 2

(3)

Step 1:

Observe the graph of the function:

We can observe from the graph that does not exists.

As tends to from the left hand side, tends to .

As tends to from the right hand side, tends to .

Since the left hand limit and right hand limit are not equal,

Limit does not exist at .

does not exist.

Solution:

does not exist.