1. Let () = { 1 + , < 1

² , 1 < 1

2 , 1 .}

a. Sketch a graph of the function f.

b. Determine lim 1 () and lim 1+ (). Show these values on the graph.

c. Explain why there is no single number that can be the limit of f(x) as x approaches -1. Write the limit statements.

d. Find lim1 () and (1). Is f continuous at x = 1? Justify your answer using the 3 conditions of continuity at a point.

e. Write the interval of continuity of f using both interval notation and set-builder notation.