Evaluating Piecewise Functions Effectively

This video tutorial by Mr. T introduces piecewise functions, explaining their definition and real-world applications. It uses examples like movie ticket pricing to illustrate how different rules apply based on input values. The tutorial covers evaluating piecewise functions, both algebraically and graphically, emphasizing the importance of understanding domain boundaries. The video concludes with a summary of key points and a preview of the next tutorial on graphing piecewise functions.

What is a piecewise function?

• A function that is always linear.

• A function that only applies to integers.

• A function defined by multiple rules, each with its own domain.

• A function defined by a single rule.

Which of the following is an example of a real-world application of piecewise functions?

• Solving quadratic equations.

• Calculating the area of a circle.

• Determining the price of movie tickets based on age.

• Finding the slope of a line.

In the movie ticket price example, what is the price for a child ticket?

• $12

• $10

• $8

• $5

What is the domain for the child ticket price rule in the movie ticket example?

• X <= 12

• X > 12

• X >= 12

• X < 12

What is a step function?

• A function where all pieces are horizontal lines.

• A function where all pieces are vertical lines.

• A function with no defined rules.

• A function that only applies to positive numbers.

When evaluating a piecewise function, what must you first determine?

• Which rule to use based on the input.

• The domain of the function.

• The slope of the function.

• The range of the function.

If f(x) is a piecewise function and x = -5, which rule should be used if the domain is x < -2?

• The rule for x < -2

• The rule for x = -2

• None of the above

• The rule for x > -2

How do you evaluate a piecewise function from a graph?

• By finding the intersection points.

• By finding the slope of the graph.

• By identifying the x-value and reading the corresponding y-value.

• By calculating the area under the graph.

What does an open circle on a graph of a piecewise function indicate?

• The function is continuous.

• The function is undefined.

• The value is not included.

• The value is included.

What is the y-value of f(x) when x = 4, given the graph of a piecewise function?

• 1

• 0

• 2

• 3