Algebra-2

Let's analyze the function step by step to determine which graph is correct:

 

 1. Simplify the function

First, factor the numerator: . Then the function can be written as:

 

For , we can cancel out the common factor , and we get . However, we need to note that there is a removable discontinuity (a hole) at because the original function was undefined at that point before the simplification.

 

 2. Analyze key features

Hole:

Since we canceled out the factor , there is a hole in the graph at . To find the -coordinate of the hole, we substitute into the simplified function , which gives . So there is a hole at the point .

 

Intercepts:

x-intercept:

Set , for the simplified function , we have , which implies