Q. 30 - Calculus

Question

Sketch the graph of a function f described in Exercises 27–32, if possible. If it is not possible, explain why not.

$f has an infinite discontinuity at 0 but is right continuous at 0, and f \left(0\right) = 1.$

Step-by-Step Solution

Answer

The graph of the given function is:

Step 1. Given Information.

Given the function has a infinite discontinuity at $x=0.$

It is right continuous at $x=0.$

And also $f\left(0\right)=1.$

Step 2. Drawing graph from the given conditions.

Now firstly point a coordinate on the graph which is (0,1).

And now as we know the graph is right continuous draw any line or curve which is continuous to the right of the point we located on the graph as given in the diagram:

Now it is clear from the graph we have $point A\equiv (0,1)$ and the graph is right continuous at $x=0.$

Step 3. Completing all the conditions to complete the graph.

Now we have one more condition to be satisfied with us which is our function has a infinite discontinuity at the point A (0,1). So, draw any continuous curve on the left side of the graph satisfying it should goes to infinity from the left side of the point A (-1,2).  As seen in the below graph: 

So, this is our final graph of the function given satisfying all the conditions.

Note: This is not a unique function for the set of conditions given in the question there may be infinite type of functions we can draw from this.