Show that the following function is discontinuous at x = 2 and continuous at x = 3.

Question

f(x) = x^2; 1≤x<2

= 3x – 4; 2≤x<4

Answer 1

f(2) = 2^2 =4 if the domain included x=2

and

f(2) = 3(2)-4 = 6-4 = 2 when x=2 if it were included in the domain

4 does not equal 2, there is a jump, from (2,2) to (2,4) a discontinuity in the graph

where a parabola crosses a line, the parabola ends at (2,4), the line begins at (2,2)

graph them and you can see the jump in y values between them

no way to draw the parabola and line by hand without lifting the pen or pencil off the paper

that makes it "discontinuous"