Exploring Piecewise Functions

The video tutorial covers piecewise functions, explaining their definition, evaluation, and graphing. It provides examples of evaluating piecewise functions based on different x values and demonstrates how to graph them by dividing the graph into parts according to domain changes. The tutorial also includes advanced graphing techniques and a real-world example of creating a piecewise function for shipping costs.

What is a piecewise function?

• A function represented by a single equation.

• A function that only has one domain.

• A function represented by at least two equations corresponding to different domains.

• A function that does not have any domain.

Which equation should be used to evaluate a piecewise function at x = 0?

• The equation for x < 0.

• The equation for x > 0.

• The equation for x between -2 and 0, inclusive.

• The equation for x > 4.

What is the first step in graphing a piecewise function?

• Draw the entire graph without any divisions.

• Divide the graph into parts of the domain by drawing vertical highlights at the change values.

• Substitute values into the equations.

• Use only closed circles for all points.

How do you represent a point where the function is not equal to a value?

• With a closed circle.

• With an open circle.

• With a square.

• With a triangle.

In the first example, what is the y-intercept of the equation used when x is less than or equal to 3?

• -2

• 0

• 1

• 3

What is the slope of the line for the equation used when x is greater than 3 in the first example?

• Negative

• Positive

• Zero

• Undefined

In the second example, what is the equation of the line between x = -4 and x = -2?

• y = 2

• y = 1

• y = 3

• y = 4

What should you do if there is an open and a closed circle at the same point?

• Erase both circles.

• Only draw the open circle.

• Only draw the closed circle.

• Draw both circles.

How much does shipping cost for purchases over $50 and up to $100?

• $10

• $12

• $8

• $6

What is the cost of shipping for purchases over $100 and up to $200?

• $6

• $8

• $10

• $12