Graphs with Absolute Values
Graphs with Absolute ValuesDraw the graphs of the following functions:1. y = | x |.2. y = | x | + x.3. y = | x | / x. 4. y = 2x – | x – 3 |.5. y = | x + 2 | – 3.6. y = | x + 1 | – | x – 1 |.7. y = | | x | – 1 | + 2.8. y = | x2 + x – 2 |.9. y = x2 – 4 | x | + 3.10. y = | x2 – 2 | x | – 3 |.11. y = ( x + 1 ) / | x |.12. y = ( | x | – 1 ) / x.Solve the equation graphically: 1. | 1 – x | = 2 – | x |.2. | |x + 2 | – 3 | = 1.Plot the following sets of points on the coordinate plane. | x | + | y | ≤ 1. x2 + y2 ≤ 2( | x | + | y | ).
Description
Problems involving absolute values are pretty common for IIT JEE. IIT aspirants must be familiar with the notion of absolute value and be fluent in applying various techniques to solve this type of problems. This tutorial develops students' ability to draw graphs involving variables with absolute values. Try to draw the graphs yourself. If you find some of the problems pretty difficult, attend my public class "Graphs with Absolutes Values" to get advantages of the various techniques that allow you to solve this type of problems effectively in a short period of time.
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