Evaluate the limit of the piecewise function

The video tutorial explains a special case of piecewise functions, focusing on graphing the function X^2 + 1 for all values except X=0, where it equals 3. The instructor discusses the concept of discontinuity, highlighting the hole at X=0 and its implications for limits and continuity. The tutorial also covers evaluating the function at X=0 and understanding its significance in the context of piecewise functions.

What is the value of the function f(x) = x^2 + 1 at x = 0?

• 0

• 3

• 1

• 2

What does the graph of f(x) = x^2 + 1 look like at x = 0?

• A horizontal line

• A vertical asymptote

• A hole

• A continuous line

What y-value does the function approach from both sides as x approaches 0?

• 3

• 2

• 1

• 0

How is the discontinuity at x = 0 described in the function f(x) = x^2 + 1?

• A continuous point

• A removable discontinuity

• A jump discontinuity

• An infinite discontinuity

What is the function value at x = 0 in the piecewise function discussed?

• 0

• 1

• 2

• 3