Piecewise Function Analysis

In this video, Anil Kumar explains how to explore the domain and range of a piecewise function. The function is defined in three parts: a linear function for x less than -2, a quadratic function for x between -1 and 2, and a constant function for x greater than 2. The video demonstrates how to sketch the function, determine its domain and range using interval notation, and identify discontinuities. The video concludes with a suggestion to practice writing domain and range in different notations.

What is a piecewise function?

• A function that has no domain.

• A function defined by a single equation.

• A function defined by multiple equations over different intervals.

• A function that is always continuous.

In the given piecewise function, what is the expression for H(x) when x is less than -2?

• H(x) = x + 2

• H(x) = 2x + 2

• H(x) = 3

• H(x) = x^2

How do you determine the values for the first piece of the function?

• By guessing the values.

• By using a calculator.

• By using a table of values.

• By drawing a random line.

What is the x-intercept of the first piece of the function?

• x = -2

• x = -1

• x = 0

• x = 2

What is the purpose of using a table of values when sketching the first piece?

• To make the graph look nice

• To accurately plot the points

• To guess the values

• To avoid using a calculator

What is the significance of an open circle in the graph of a piecewise function?

• It indicates a point is included.

• It indicates a minimum point.

• It indicates a point is not included.

• It indicates a maximum point.

What is the y-intercept of the first piece of the function?

• 3

• 0

• 1

• 2

What is the slope of the line in the first piece of the function?

• 3

• 1

• 0

• 2

What is the expression for the second piece of the function?

• H(x) = x + 2

• H(x) = 2x + 2

• H(x) = x^2

• H(x) = 3

What is the value of H(x) at x = 0 for the second piece?

• 2

• 3

• 0

• 1