How to Graph a Piecewise Function Step-by-Step

TL;DR

To graph a piecewise function, identify the different intervals defined by the function and plot their endpoints. Connect the points according to the defined lines for each interval, being careful to note whether the endpoints are included in the graph. Accuracy in plotting is key to effectively visualizing the piecewise function.

Transcript

• [Voiceover] So, I have this somewhat hairy function definition here, and I want to see if we can graph it. And this is a piecewise function. It's defined as a different, essentially different lines. You see this right over here, even with all the decimals and the negative signs, this is essentially a line. It's defined by this line over this inte... Read More

Key Insights

• 🫥 Piecewise functions consist of different lines over specific intervals, allowing for more complex mathematical representations.
• 🫥 Graphing a piecewise function requires plotting the endpoints and connecting them to form the lines.
• 😥 The points where two intervals meet need to be handled carefully, as they may or may not be included in the function.

Questions & Answers

Q: How can a piecewise function be graphed?

To graph a piecewise function, plot the endpoints of each interval and connect them to create the corresponding lines.

Q: What is the graph of the first interval of the provided piecewise function?

The first interval is defined by the line -0.125x plus 4.75. By evaluating the function at x = -10 and x = -2, we find the points (-10, 6) and (-2, 5), respectively. Connecting these two points produces a downward sloping line.

Q: How is the second interval of the piecewise function graphed?

The second interval is defined by the line -2 plus seven. Thus, at x = -2, the graph includes the point (-2, 5). Since x = -1 is not included, an open circle is placed at (-1, 6). The line passing through (-2, 5) and approaching (-1, 6) is drawn.

Q: What are the endpoints and corresponding y-values for the last interval?

The last interval is defined by positive 12 over 11 times x plus 54 over 11. Evaluating the function at x = -1 and x = 10, we obtain the points (-1, 6) and (10, -6), respectively.

Summary & Key Takeaways

• The provided content demonstrates how to graph a piecewise function consisting of different lines over specific intervals.

• The function is defined by negative 0.125x plus 4.75 for x values between -10 and -2, negative two plus seven for x values between -2 and -1, and positive 12 over 11 times x plus 54 over 11 for x values greater than -1.

• By plotting the endpoints and connecting them with lines, the graph of the piecewise function can be accurately drawn.