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To solve for the value of p that makes the piecewise function continuous, first look at the domain restrictions to see that the functions need to meet when x=3. Then set the two functions equal to each other and plug x=3 into the equations to solve for p. Doing this reveals that when p=1/3, the functions will meet at the same y-coordinate and the piecewise function will be continuous.
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This document provides examples for representing and analyzing linear functions using equations, tables, graphs and words. It begins by showing how to write an equation to represent the relationship between quarts and liters of liquid. It then demonstrates how to find the rate of change or slope of a linear function from its graph or two points. The document continues with examples of making function tables, evaluating functions, comparing functions in different forms, and interpreting the rate of change and initial value of linear functions.
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Ncfe afm question
- 1. How to solve the NC Final Exam question:
- 2. Piecewise Functions Review Remember, a piecewise function is where multiple functions are graphed for certain domain values. In this question, we want to find the value of p that will make this function continuous, meaning the red and blue functions will touch.
- 3. Look at the domain restrictions First, look at the domain restrictions. The first function is defined for values less than 3 and the second function is defined for values larger than or equal to 3. That means they need to meet, or have the same y- coordinate, when x = 3. If we want them to have the same y- coordinate, then we set the functions EQUAL to each other and plug in x=3.
- 4. Set the equations equal to each other
- 5. Plug in x = 3
- 6. Solve for p.
- 7. So when p=1/3, the two functions will meet in the same place, making our piecewise function continuous!