Piecewise Function Analysis

The video tutorial explains how to write a piecewise function to describe a graph with four segments. Each segment is analyzed for its slope, y-intercept, and domain. The tutorial also covers transformations of the piecewise function, including horizontal shifts and stretches. The use of a calculator for algebraic calculations is demonstrated to simplify the process.

What is the main task described in the introduction of the video?

• To write a piecewise function for a graph

• To calculate the area under a curve

• To solve a quadratic equation

• To find the derivative of a function

What is the slope of the first segment of the piecewise function?

• 3/4

• 2/3

• 1/3

• 1/2

What is the domain of the first segment of the piecewise function?

• t is between 45 and 65

• t is between 15 and 45

• t is between 65 and 110

• t is between 0 and 15

What is the nature of the second segment of the piecewise function?

• It is a vertical line

• It is a horizontal line

• It is a diagonal line

• It is a curved line

What is the y-value for the second segment of the piecewise function?

• 20

• 10

• 15

• 5

What is the domain of the second segment of the piecewise function?

• t is between 0 and 15

• t is between 15 and 45

• t is between 45 and 65

• t is between 65 and 110

How is the slope of the third segment calculated?

• Using a calculator

• Using a ruler

• Using a graph

• Using a protractor

What is the slope of the third segment?

• 1.1

• 0.9

• 0.7

• 0.5

What is the y-intercept of the third segment?

• 0

• -30.5

• -20.5

• -10.5

What is the domain of the third segment of the piecewise function?

• t is between 65 and 110

• t is between 45 and 65

• t is between 15 and 45

• t is between 0 and 15