Sketch the graph of an example of a function f that satisfies all of the given conditions

Question

f(-1.5) = 1, f(0) = 2, f(3) = 0, lim x ---->2+ f(x)= -infinity, lim x---->0- f(x)= 2, lim x---->0+ f(x)= infinity 

Any help would be appreciated. Thanks!

Answer 1

Step 1:

The expressions are 

Consider

As  tends to  from right hand side, the function  approaches to

Consider

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

Consider

As  tends to  from right hand side, the function  approaches to

The graph values are

Graph the function such that all the conditions are satisfied.

Note: The solid circle indicates the value of the function.

Solution:

Graph of the function is drawn such that all the conditions are satisfied.