How to Graph a Piecewise Function and Determine Domain and Range

The video tutorial covers graphing linear equations in slope-intercept form, y=mx+b, and explores graphing piecewise functions with domain restrictions. It explains how to plot y-intercepts and slopes, and discusses the concept of discontinuities, specifically jump discontinuities. The tutorial also guides students in identifying the domain and range of functions, emphasizing the impact of open and closed circles on these properties.

What is the first step in graphing a line in slope-intercept form?

• Plot the y-intercept

• Plot the x-intercept

• Calculate the slope

• Draw a horizontal line

How can you rewrite the equation y = -2x - 2 to make it easier to graph?

• y = 2x + 2

• y = -2x + 2

• y = -2x - 2

• y = 2x - 2

What is a key characteristic of a piecewise function?

• It has a single continuous line

• It is graphed on separate axes

• It has different rules for different parts of its domain

• It is always increasing

When graphing a piecewise function, what does an open circle indicate?

• The function has a maximum at that point

• The function is continuous at that point

• The point is not included in the domain

• The point is included in the domain

What is the domain of a piecewise function?

• The slope of the function

• The range of the function

• The set of all possible x-values

• The set of all possible y-values

What is a jump discontinuity?

• A point where the function is continuous

• A point where the function changes abruptly

• A point where the function is undefined

• A point where the function has a maximum

How does a hole in the graph affect the domain?

• It does not affect the domain

• It makes the domain infinite

• It excludes the point from the domain

• It includes the point in the domain