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3.3 Library of Functions, Piecewise-Defined Functions

3.3 Library of Functions, Piecewise-Defined Functions. A linear function is a function of the form. f(x)=mx+b. The graph of a linear function is a line with a slope m and y- intercept b. (0,b). A constant function is a function of the form. f(x)=b. y. b. x.

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3.3 Library of Functions, Piecewise-Defined Functions

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  1. 3.3Library of Functions, Piecewise-Defined Functions

  2. A linear function is a function of the form f(x)=mx+b The graph of a linear function is a line with a slope m and y-intercept b. (0,b)

  3. A constant function is a function of the form f(x)=b y b x

  4. Identity function is a function of a form: f(x)=x (1,1) (0,0)

  5. The square function

  6. Cube Function

  7. Square Root Function

  8. Reciprocal Function

  9. Absolute Value Function f(x) = |x|

  10. When functions are defined by more than one equation, they are called piece-wise defined functions.

  11. For the following function a) Find f(-1), f(1), f(3). b) Find the domain. c)Sketch the graph.

  12. a) f(1) = 3 f(-1) = -1 + 3 = 2 f(3)= -3 + 3 = 0 b)

  13. c)

  14. Piece-wise defined functions are easy to graph with your TI-83. • Select Dot mode • Turn off other functions • Y1=(x+3)(-2 <x)(x < 1)+(3)(x = 1)+(-x + 3)(x > 1)

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