Lesson 12 · Continuity and Discontinuity of a Function
Continuity and Discontinuity of a Function
Optional MathematicsSubject
8 minEstimated read
Activity 1
Is the graph broken?
Method
Observe the graph of \( y = x^2 \) (Figure 1).
Observe the graph of \( y = \frac{x^2 - 4}{x - 2} \) (Figure 2).
Discuss the questions below.
Discussion
Is the curve in the graph of Figure 1 broken anywhere?
In the graph of Figure 2, is the line broken at \( x = 2 \)?
If \( y = \frac{x^2 - 4}{x - 2} \), what is the value of \( y \) when \( x = 2 \)? In that case, can the point \( (x, y) \) be shown on the graph? Is the graph joined or broken at \( x = 2 \)? Give your reasons.
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