Question

Math

Determine if the function below is continuous.

graph of a piecewise function, with 2 pieces. The first piece is a line that starts at negative infinity and goes through point (-4,5) and ends with an open dot at (1,0). The second piece is a line that starts with a closed dot at (1,-1), goes through point (2,1) and continues to infinity.

A. not continuous at x = 1
B. not continuous at x = 0
C. not continuous at x = -1
D. continuous

Answer 1

The function is not continuous at x=1, so the answer is A.

At x=1, the two pieces of the function meet. The first piece ends with an open dot at (1,0), meaning that the function is not defined at $x=1$. The second piece starts with a closed dot at (1,-1), meaning that the function is defined at x=1 and takes the value -1 there.

Since the function is not defined at x=1, it cannot be continuous at that point. Therefore, the function is not continuous overall.