1If a curve can be drawn without lifting the pen, what is it called? (a) discontinuous curve (b) continuous curve (c) broken curve (d) cut curve
2Which of these can be an example of continuity in daily life? (a) the height of a plant increasing (b) a cricket score increasing (c) the number of students in a class (d) the number of coins in a pocket
3Which part of the number line do the real numbers from -2 to +2 occupy? (a) some points between -2 and +2 (b) all the points from -2 to +2 (c) only the points -2, 0 and +2 (d) all the points -2, -1, 0, +1, +2
4Which condition is necessary for a function to be continuous at x = a? (a) the graph must be cut at x = a (b) the graph must be broken at x = a (c) the graph must not be broken at x = a (d) the graph must have a hole at x = a
5What does it mean for a curve to be continuous or discontinuous? Explain with examples.
6What does it mean to say that a curve is continuous from -5 to +5? Show it with a figure.
7A curve starts at a filled dot at x = -4, rises, has an open circle at x = 3, and ends at a filled dot at x = 5. From which point to which point is it continuous, and where is it discontinuous?
8A graph is made of two straight pieces. The lower piece rises from x = -1 to x = 1. The upper piece starts at an open circle above x = 1 and rises to x = 5. Where is it continuous, and where is it discontinuous?
9A curve starts at an open circle at x = -1, rises and turns steeply upward near x = 3, running off the top of the grid. A separate piece of curve begins again to the right of x = 3. Where is the curve continuous, and where is it discontinuous?
10In a house, wire A is straight and not broken anywhere, so current flows through it all the time. Is wire A continuous or discontinuous? Give a reason.
11Wire B is bent sharply at a right angle at the corner of a room, at x = 3, but it is not cut inside. Is wire B continuous or discontinuous at x = 3? Give a reason.
12Wire C has been bitten through by a rat, or has worn out, exactly 4 metres along (x = 4), so the current stops there. In mathematical language, what is the cut part at x = 4 called?
13Compare wire B (the sharp bend) with wire C (the cut wire). In which case is the function, the flow of current, continuous and in which is it discontinuous? Why does bending a wire sharply not break continuity?
14Why do the integers not form a continuous line, while the real numbers do?
15A student reads a curve that starts at a filled dot at x = -4, has an open circle at x = 1, and ends at a filled dot at x = 4, and writes that it is continuous on \( -4 \le x \le 1 \). What is wrong, and what is the correct answer?
16Can the outline of a cross shape be drawn without lifting the pen? Is it a continuous or a discontinuous figure?