Graphing Piecewise Functions: Key Concepts and Techniques

What is the first step in graphing a piecewise function?

• Determine the behavior of each piece

• Plot the graph

• Identify the intervals

• Check the border points

How many pieces does the given piecewise function have?

• Three

• Four

• One

• Two

What type of graph does the expression y = x + 1 represent?

• Parabola

• Linear line

• Horizontal line

• Vertical line

Which expression represents a horizontal line?

• y = x - 1

• y = x^2

• y = 5

• y = x + 1

In which interval does the function behave like y = x + 1?

• x < -3

• x > 0

• x = 0

• x between -3 and 0

What does the function look like for x values between -3 and 0?

• Vertical line

• Linear line

• Parabola

• Horizontal line at y = 5

Where should the line y = x + 1 be drawn on the graph?

• Everywhere

• Only in the section where x < -3

• Only in the section where x > 0

• Only in the section where x = 0

What type of graph does the expression y = x^2 represent?

• Parabola

• Horizontal line

• Linear line

• Vertical line

What should be placed at the point where x = -3 on the graph?

• No circle

• Solid circle at the lower piece

• Open circle at the upper piece

• Solid circle at the upper piece

What should be placed at the point where x = 0 on the graph?

• No circle

• Solid circle at the lower piece

• Open circle at the upper piece

• Solid circle at the upper piece