Graphing piecewise functions
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ISRO CS Syllabus for Scientist/Engineer Exam.ISRO CS Original Papers and Official Keys.GATE CS Original Papers and Official Keys.Describe the process of graphing piecewise functions to your friend who was absent today in student friendly language. Example 3: Graph ? ? =2 ? +2 Create a t-table Plot the points as you go until you see the “v” ? ? ? +? What are the two linear equations that would be the pieces? What would the boundary be? ? ? = 2 ? −? +2 ? ? = 2?+2 ?≥0 −2?+2 ? and ≤≥.
![graphing piecewise functions graphing piecewise functions](https://i.ytimg.com/vi/uX1p1S3QdR4/maxresdefault.jpg)
Students will be able to Identify and Graph piecewise functions (including absolute value) as evidenced by a math journal. We will see later that we can have quadratic, cubic, etc absolute value also.ĩ Example 3: Graph ? ? =2 ? +2 Create a t-table The more comfortable you are graphing absolute value, the fewer numbers you will need to plot For our purposes in THIS SECTION, we will be working with LINEAR absolute value. How do I graph absolute value? Create a t-table and start plotting points, your goal is to see that absolute values “v”, since you are piecing together two linear functions, once you find where the sharp turn happens you can use a ruler to continue the line. ? means −(?)AND ? since they are both the same distance from zero. As we progress through this course we will see what || means in higher dimensions. In one dimension we usually say “|−3| means how far is −3 away from zero?” and we say 3, so |−3|=3. What is absolute value? Absolute value || is the SIZE or a number (one, two, three dimensional). Know the difference between the symbols means NOT included so we use and OPEN circle ≤≥ means included, so we use a CLOSED circle Understand what the boundaries mean, four types ?>? all values to the right of a ?3 How do we graph piecewise functions? Use multiple colors if you have them, one color for each piece. Need at least two points Linear ??+?, what is the slope? What is the y intercept? Need at least 2 points Quadratic ? ? 2 +??+? or ? ?−ℎ 2 +? whose vertex is (ℎ, ?) and ? determines directions of opening (up or down) and compression (wide or skinny) Need at least three points Cubic ? ? 3 where ? is the directions of opening and compression, need three points
![graphing piecewise functions graphing piecewise functions](https://i.ytimg.com/vi/mrfCcU0QV-U/maxresdefault.jpg)
What common functions are used to “piece” together? Constant Just a number, looks like a horizontal line. “Frankenstein Functions”ģ What common functions are used to “piece” together? What is a piecewise function? A piecewise function (passes vertical line test) is a function that is made up of different graphs for different intervals.
![graphing piecewise functions graphing piecewise functions](https://mszeilstra.weebly.com/uploads/4/8/8/8/48889683/8872829_orig.png)
1 1.7 Piecewise Functions Students will be able to Identify and Graph piecewise functions (including absolute value) as evidenced by a math journal.