Edge Cases Math Example 1

Follow the full solution, then compare it with the other examples linked below.

easy

For the function

f(x) = \dfrac{x^2-4}{x-2}

, check the edge case

x = 2

and describe what happens.

1
At $x = 2$ : the denominator $x - 2 = 0$ , so $f(2)$ is undefined — this is the edge case.
2
For $x \ne 2$ : factor the numerator — $\frac{x^2-4}{x-2} = \frac{(x-2)(x+2)}{x-2} = x + 2$ .
3
So $f(x) = x+2$ for all $x \ne 2$ . There is a hole in the graph at $x=2$ , $y=4$ .

Answer

f(x) = x+2 \text{ for } x \ne 2;\quad f(2) \text{ is undefined (hole at }(2,4)\text{)}

Edge cases are special inputs where a formula breaks or behaves differently. Checking

x = 2

(where the denominator vanishes) is essential for understanding the full behaviour of

f

About Edge Cases

Special or extreme input values — such as zero, infinity, empty sets, or boundary conditions — where formulas or reasoning may behave differently.

Check all edge cases for the statement: 'For natural numbers [formula], [formula].' Test [formula] a

For [formula], identify the edge case and state the domain.

Test the edge cases [formula] and [formula] for the formula [formula].