Graphing and evaluating piecewise functions

The video tutorial covers piecewise functions, including their notation, graphing, evaluation, and continuity. It explains how to graph piecewise functions with domain constraints, evaluate them at specific points, and determine the value of K for continuity. The tutorial also addresses common student mistakes and provides an algebraic method for finding K. The session concludes with a recap and a Q&A segment.

What is a piecewise function?

• A function with no domain restrictions

• A function defined by a single equation

• A function that is always continuous

• A collection of two or more functions

Which of the following is a characteristic of an exponential function?

• It has a V shape

• It has a horizontal asymptote

• It is always linear

• It is undefined for negative values

How is the absolute value function graphically represented?

• As a straight line

• As a V shape

• As a parabola

• As a circle

What is the domain of the piecewise function discussed?

• All real numbers

• Only positive numbers

• Numbers greater than 1

• Only negative numbers

When evaluating F(-1), which function should be used?

• The exponential function

• The absolute value function

• Both functions

• Neither function

What is the value of K that makes the piecewise function continuous?

• 1

• 2

• -1

• 0

How can you algebraically ensure two piecewise functions are continuous at a point?

• By making sure they have the same range

• By setting their Y values equal at that point

• By ensuring they have the same domain

• By setting their derivatives equal