Diagrammatic Representation of Functions.ppt
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A relation as a function provided there is exactly one output for each input. It is NOT a function if at least one input has more than one output A function is to have a limit if it has a two-sided limit. A graph provides a visual method of determining the limit of a function. If the function has a limit as x approaches a, the branches of the graph will approach the same y-coordinate near x=a from the left and the right. Consider functions f :A (⊂ X) → Y where X and Y are metric spaces. Important cases are 1. f :A (⊂ R) → R, 2. f :A (⊂ Rn) → R, 3. f :A (⊂ Rn) → Rm Sometimes we can sketch the domain and the range of the function, perhaps also with a coordinate grid and its image.Sometimes we can represent a function by drawing a vector at various points in its domain to represent f(x). We can represent a real-valued function by drawing the level sets (contours) of the function. In other cases the best we can do is to represent the graph, or the domain and range of the function, in a highly idealized manner..Sometimes we can represent a function by drawing a vector at various points in its domain to represent f(x).
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A function is a set of ordered pairs where each x-value is paired with exactly one y-value. The domain is the set of all possible x-values, and the range is the resulting y-values. To find the rate of change, use the difference quotient which is similar to the slope formula. The vertical line test determines if a graph represents a function - if any vertical line intersects the graph more than once, it is not a function. Domain restrictions specify allowed input values.
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9
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structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
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𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
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- 1. Diagrammatic Representation of Functions MA. SHARON M. ARTILLO MILE Math
- 2. Functions Page 116 •A relation as a function provided there is exactly one output for each input. •It is NOT a function if at least one input has more than one output
- 3. INPUT (DOMAIN) OUTPUT (RANGE) FUNCTION MACHINE In order for a relationship to be a function… EVERY INPUT MUST HAVE AN OUTPUT TWO DIFFERENT INPUTS CAN HAVE THE SAME OUTPUT Functions ONE INPUT CAN HAVE ONLY ONE OUTPUT
- 4. A function is to have a limit if it has a two-sided limit. A graph provides a visual method of determining the limit of a function. If the function has a limit as x approaches a, the branches of the graph will approach the same y-coordinate near x=a from the left and the right.
- 7. Important cases are 1. f :A (⊂ R) → R, 2. f :A (⊂ Rn) → R, 3. f :A (⊂ Rn) → Rm Consider functions f :A (⊂ X) → Y where X and Y are metric spaces.
- 8. Functions can be quite complicated, and we should be careful not to be misled by the simple features of the particular graphs which we are able to sketch. We can represent a function by its graph
- 9. 1. f :A (⊂ R) → R,
- 12. Sometimes we can sketch the domain and the range of the function, perhaps also with a coordinate grid and its image.
- 13. Sometimes we can represent a function by drawing a vector at various points in its domain to represent f(x).
- 14. We can represent a real-valued function by drawing the level sets (contours) of the function. In other cases the best we can do is to represent the graph, or the domain and range of the function, in a highly idealised manner..
- 15. THANK YOU
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- 17. THANK YOU
- 18. THANK YOU
- 19. THANK YOU