Limit of a piecewise function left, right and general where there is a hole

The video tutorial explains the concept of function discontinuity, focusing on the difference between holes and asymptotes. It demonstrates how to simplify a function to identify a hole and graph it accurately. The tutorial also covers the concept of limits, showing how to approach a function's value from different sides. It addresses common graphing mistakes and emphasizes the importance of simplification for direct substitution. The video concludes with a discussion on the difference between a function's value and its limit.

What type of discontinuity is present in the function 2X^2 + X / X?

• A jump discontinuity

• A hole

• A removable discontinuity

• An asymptote

What does the graph of the simplified function 2X + 1 look like?

• A parabola with a hole

• A line with a hole

• A curve with an asymptote

• A line with a jump

As the function approaches zero from both sides, what value does it approach?

• 3

• 0

• 1

• -1

Why is it important to simplify a function before applying direct substitution?

• To find the exact value of the function

• To identify the type of discontinuity

• To apply direct substitution correctly

• To ensure the function is continuous

What is the difference between the value of a function and its limit at a point?

• The value is always less than the limit

• The limit is what the function approaches, while the value is the actual output

• There is no difference

• The value is always greater than the limit