Exploring Piecewise Functions

Miss Smith's math tutorial covers piecewise functions, explaining how to graph, evaluate, and write them. The video begins with an introduction to piecewise functions, followed by a detailed guide on graphing them using T-charts and graphing calculators. It then demonstrates how to evaluate piecewise functions using both equations and graphs. Finally, the tutorial explains how to write piecewise functions from given graphs, emphasizing the importance of understanding slopes, intercepts, and restrictions.

What is a piecewise function?

• A function that is continuous and differentiable everywhere.

• A function that is always linear.

• A function that is defined by multiple sub-functions, each applying to a certain interval of the main function's domain.

• A function that only has one equation.

What does the equation y = 2 represent in the context of piecewise functions?

• A vertical line at x = 2

• A diagonal line with a slope of 2

• A parabolic curve

• A horizontal line at y = 2

How do you determine if a point is included in a piecewise function?

• By checking if the inequality symbol includes an 'or equal to' line

• By looking at the color of the point

• By checking if the point is at the origin

• By seeing if the point is on the x-axis

What is the equation for the second piece of the function if x falls between -1 and 4?

• y = 2x + 1

• y = -x + 4

• y = 3x - 9

• y = x^2 + 3

What is the value of f(3) for the given piecewise function?

• 1

• 3

• 0

• 2

Which equation would you use to evaluate f(-4)?

• y = -x + 4

• y = 2x + 1

• y = 3x - 9

• y = 2

What is the domain of the given piecewise function?

• (-∞, 4]

• (-∞, ∞)

• [0, ∞)

• [-1, 4]

What is the range of the given piecewise function?

• [0, 2]

• (-∞, 0]

• [0, ∞)

• [0, ∞)

How do you write the equation of a horizontal line in a piecewise function?

• y = mx + b

• y = 3x - 9

• y = a constant value

• y = x^2 + c

What is the slope of the line y = x + 5?

• 0

• -1

• 1

• 5