Tell whether if the following piecewise function is a continuous at a given point or not.

Question

Tell whether if the following piecewise function is a continuous at a given point or not. (SHOW THE SOLUTION).

1. at x = 4

x + 1 if x < 4

(x - 4)² + 3 if x ≥ 4

Answer 1

(x-4)^2 -3 = (4-4)^2 -3 = 0-3 = -3

x+1 = 4+1 = 5

the stepwise function is discontinuous at x=4

it jumps from y=5 to y =-3

it's an upward sloping line to the left of x=4

it's an upward opening parabola with vertex at (4,-3)

the stepwise function jumps downward by 8 units at x=4

(x-4)^2 -3 = x^2 -8x -16x+9 = x^2 +16x +9 = x+1

x^2 -17x +8 = 0

x =about .5 and 16.5, the two places where the graph meets

at x=4, the two graphs are 8 units apart