Piecewise Functions and Graphing Concepts

This video tutorial covers the graphing of piecewise defined functions both manually and using a graphing calculator. It begins with an introduction to piecewise functions, explaining how they change rules based on input values. The tutorial then provides a detailed guide on graphing these functions by hand, followed by instructions on using a graphing calculator for the same purpose. Advanced techniques for graphing more complex piecewise functions are also discussed, including handling functions with multiple segments. The video concludes with practical examples and verification methods.

What is a piecewise defined function?

• A function that cannot be graphed

• A function that only uses linear equations

• A function with multiple rules depending on the input value

• A function with a single rule for all inputs

When graphing the first rule of a piecewise function by hand, what should you do if the inequality does not include the boundary point?

• Ignore the boundary point

• Use a different color

• Use an open point

• Use a closed point

What is the slope of the line y = -x + 2?

• 2

• -1

• 1

• -2

How do you determine which part of the graph to keep when graphing a piecewise function?

• Erase the part that is below the x-axis

• Keep the entire graph

• Erase the part that does not satisfy the inequality

• Keep only the part that is above the x-axis

What is the y-intercept of the function y = 2x - 1?

• -1

• 1

• 0

• 2

How can you verify a piecewise function graph using a graphing calculator?

• By ignoring the inequalities

• By using only the first rule

• By drawing the graph manually

• By entering each rule separately and using inequalities

What is the shape of the graph for the function y = -x^2 - 1?

• A circle

• A straight line

• A parabola opening downwards

• A parabola opening upwards

When graphing y = x^2 + 1, what transformation is applied to the basic parabola y = x^2?

• Shifted down 1 unit

• Shifted up 1 unit

• Shifted left 1 unit

• Shifted right 1 unit

In a piecewise function with three pieces, what does the second rule represent if it is a single point?

• A parabola

• A circle

• A single point on the graph

• A line segment

When using a graphing calculator, what is a limitation you must be aware of?

• It does not show open or closed points clearly

• It cannot handle inequalities

• It only graphs linear functions

• It cannot graph piecewise functions