Gr10 piecewise functions
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This document discusses different types of piecewise functions including: - Piecewise functions which use separate equations depending on the domain values. For example, one equation for when x ≤ 1 and another for when x > 1. - An example problem evaluating a piecewise function at different x values and determining which equation to use. - Graphing a piecewise function involves using one equation's graph for values below a breaking point, and another equation's graph for values at or above the breaking point. - Greatest integer functions which return the greatest integer less than or equal to the input value. An example graph of y = [x] + 2 is shown and evaluated in a table.
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1 13s-f
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More: www.PinoyBIX.org
Lesson Objectives
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Graph of Cosine Function (y = f(x) = cosx)
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Graphs of y = sin(bx + c)
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1. A function is a relationship between inputs and outputs where each input corresponds to exactly one output. The domain of a function is the set of possible inputs, and the range is the set of possible outputs.
2. For a function to be one-to-one, each output must correspond to only one input. This can be tested using the horizontal line test - drawing horizontal lines on the graph. Restricting the domain can make non-one-to-one functions one-to-one.
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Functions and Their Graphs
Calculus - 1 Functions, domain and range
This document defines functions and discusses key concepts related to functions including:
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- The domain of a function is the set of possible inputs, and the range is the set of possible outputs.
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AS LEVEL Function (CIE) EXPLAINED WITH EXAMPLE AND DIAGRAMS
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Gr10 piecewise functions
- 1. Algebra II Piecewise Functions Edited by Mrs. Harlow
- 3. Constant Function: A linear function in the form y = b. y = 3
- 4. Identity Function: A linear function in the form y = x. y=x
- 9. x=1 is the breaking point of the graph. To the left is the top equation. To the right is the bottom equation.
- 10. Graph:
- 13. Step Functions
- 15. Graph :
- 18. Assignment