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Topic: U5L3 Graphing Piecewise Functions

Topic: U5L3 Graphing Piecewise Functions. EQ: What are piecewise functions and how do I graph them?. Library of Functions. You should be familiar with the shapes of these basic functions. We'll learn them in this section. Linear Functions.

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Topic: U5L3 Graphing Piecewise Functions

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  1. Topic: U5L3 Graphing Piecewise Functions EQ: What are piecewise functions and how do I graph them?

  2. Library of Functions You should be familiar with the shapes of these basic functions. We'll learn them in this section.

  3. Linear Functions Equations that can be written f(x) = mx + b slope y-intercept The domain of these functions is all real numbers.

  4. f(x) = 3 f(x) = -1 f(x) = 1 Constant Functions f(x) = b, where b is a real number The domain of these functions is all real numbers. The range will only be b

  5. If you put any real number in this function, you get the same real number “back”. f(x) = x Identity Function f(x) = x, slope 1, y-intercept = 0 The domain of this function is all real numbers. The range is also all real numbers

  6. Quadratic Function f(x) = x2 The domain of this function is all real numbers. The range is

  7. Cubic Function f(x) = x3 The domain of this function is all real numbers. The range is all real numbers

  8. Square Root Function The domain of this function is The range is

  9. Absolute Value Function The domain of this function is all real numbers. The range is

  10. These are functions that are defined differently on different parts of the domain. WISE FUNCTIONS

  11. This means for x’s less than 0, put them in f(x) = -x but for x’s greater than or equal to 0, put them in f(x) = x2 What does the graph of f(x) = -x look like? What does the graph of f(x) = x2 look like? Remember y = f(x) so let’s graph y = - x which is a line of slope –1 and y-intercept 0. Remember y = f(x) so lets graph y = x2 which is a square function (parabola) Since we are only supposed to graph this for x< 0, we’ll stop the graph at x = 0. Since we are only supposed to graph this for x 0, we’ll only keep the right half of the graph. This then is the graph for the piecewise function given above.

  12. For x > 0 the function is supposed to be along the line y = - 5x. For x = 0 the function value is supposed to be –3 so plot the point (0, -3) For x values between –3 and 0 graph the line y = 2x + 5. Since you know the graph is a piece of a line, you can just plug in each end value to get the endpoints. f(-3) = -1 and f(0) = 5 Since you know this graph is a piece of a line, you can just plug in 0 to see where to start the line and then count a – 5 slope. open dot since not "or equal to" So this the graph of the piecewise function solid dot for "or equal to"

  13. Acknowledgement I wish to thank Shawna Haider from Salt Lake Community College, Utah USA for her hard work in creating this PowerPoint. www.slcc.edu Shawna has kindly given permission for this resource to be downloaded from www.mathxtc.com and for it to be modified to suit the Western Australian Mathematics Curriculum. Stephen Corcoran Head of Mathematics St Stephen’s School – Carramar www.ststephens.wa.edu.au

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