Evaluating Piecewise Functions Effectively

This video tutorial introduces piecewise functions, explaining their structure and how they are composed of different function pieces. It covers the concept of open and closed circles in graphs, which indicate whether a point is included or excluded. The tutorial demonstrates how to evaluate piecewise functions using both graphs and equations, emphasizing the importance of understanding the domain and selecting the correct equation based on inequalities. The video provides examples to illustrate these concepts, ensuring a comprehensive understanding of piecewise functions.

What is a piecewise function?

• A function with repeating x-values.

• A function that does not pass the vertical line test.

• A function made up of different pieces of functions.

• A function with a single equation.

What does a closed circle on a piecewise graph represent?

• The point is not included.

• The point is included.

• The function is undefined at that point.

• The function has a vertical asymptote.

What does an open circle on a piecewise graph indicate?

• The point is not included.

• The function is continuous at that point.

• The point is included.

• The function has a horizontal asymptote.

How do you evaluate f(-5) using a piecewise graph?

• Find the y-value at x = -5.

• Find the intercept of the line at x = -5.

• Find the x-value at y = -5.

• Find the slope of the line at x = -5.

Which point do you choose if there is both an open and closed circle at the same x-value?

• The closed circle.

• The midpoint between the circles.

• The open circle.

• Neither point.

What is the value of f(1) if the point on the graph is (1, 1)?

• 3

• 1

• 2

• 0

How do you determine which equation to use when evaluating a piecewise function?

• By choosing the equation with the highest degree.

• By using all equations simultaneously.

• By choosing the equation with the smallest coefficient.

• By selecting the equation based on the domain of the x-value.

What is the value of f(-5) if the equation for x ≤ -3 is 2x + 1?

• 9

• -10

• 10

• -9

Which equation do you use for f(1) if the domain is -3 < x ≤ 3?

• The equation for x ≤ -3.

• The equation for -3 < x ≤ 3.

• The equation for x > 3.

• None of the above.

What is the value of f(4) if the equation for x > 3 is a constant 4?

• 8

• -4

• 0

• 4