Determine if a piecewise function is continuous or discontinuous

The video tutorial explains how to graph a quadratic function and a linear function, focusing on understanding the effects of restrictions on these graphs. It highlights the importance of recognizing where functions are defined and how to handle piecewise functions to ensure continuity. The tutorial emphasizes that piecewise functions can be continuous if properly defined.

What effect does the '-1' have on the quadratic function X^2 - 1?

• It shifts the graph to the left.

• It shifts the graph to the right.

• It shifts the graph upwards.

• It shifts the graph downwards.

For which X values is the quadratic function X^2 - 1 defined?

• X values less than -1

• X values equal to -1

• All X values

• X values greater than -1

At X = -1, what is the value of the quadratic function X^2 - 1?

• -1

• 0

• 1

• 2

What is the main characteristic of a piecewise function that makes it continuous?

• It has no restrictions.

• The functions meet at a defined point.

• It is only defined for positive X values.

• It is a combination of linear functions.

Why is there no open hole at X = -1 in the piecewise function?

• Because both functions are undefined there.

• Because it is a point of discontinuity.

• Because the quadratic function is defined there.

• Because the linear function is defined there.