Understanding Piecewise Functions

The video tutorial explains how to write a piecewise function from a graph with three distinct pieces. It covers the identification and formulation of equations for each piece, including a horizontal line, a line with a positive slope, and a line with a negative slope. The tutorial also discusses the conditions under which each equation is valid, based on the graph's characteristics.

What is the main topic of the video tutorial?

• How to integrate a function

• How to find the derivative of a function

• How to write a piecewise function from a graph

• How to solve quadratic equations

How many pieces does the piecewise function in the video have?

• Two

• One

• Four

• Three

What is the equation of the first piece of the piecewise function?

• y = 0

• y = -1

• y = x

• y = 1

For which values of x is the first piece of the piecewise function valid?

• x ≤ -2

• x ≥ -2

• x > -2

• x < -2

What indicates that the first piece of the function includes x = -2?

• A solid line

• A dashed line

• A filled circle

• An open circle

What form is used to write the equation of the second piece of the function?

• Standard form

• Vertex form

• Slope-intercept form

• Quadratic form

What is the slope of the second piece of the piecewise function?

• 2

• 1

• 1/2

• -1

What is the y-intercept of the second piece of the piecewise function?

• 1

• 0

• 2

• -1

For which range of x is the second piece of the piecewise function valid?

• x ≤ -2

• x > 0

• x < -2

• -2 < x ≤ 0

What is the equation of the third piece of the piecewise function?

• y = -1/2x + 2

• y = 2x + 1

• y = x - 2

• y = -x + 1