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Determining Domain and Range of a Function Graph

Determining Domain and Range of a Function Graph
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2015-09-25 23:18
FunctionCoordinate GeometryGraphing
In collections CCSS Support Math II Unit 2
This example demonstrates how to plot a function graph using GeoGebra and determine its domain and range. Key math concepts include function graph, domain, range, and coordinate geometry. Construction highlights involve commands like LaTeX, Segment, Polygon, and Intersect, along with objects such as Border and Slider. Suitable for high school mathematics teaching on function graph analysis and domain/range calculation.

GeoGebra Commands & Parameters

  1. LaTeX("\text{Determine the domain and range of the following graph. }") → QuestionText
  2. LaTeX("\text{Determine the domain of the function.}") → text2
  3. LaTeX("\text{Determine the range of the function.") → text9
  4. LaTeX("\text{The domain is the set of \textcolor{#000099}{x}-values that are valid for the function. }") → text3
  5. LaTeX("\text{domain because the function is only valid when \textcolor{#000099}{x} is greater than or }") → text6
  6. LaTeX("\text{The range is the set of \textcolor{#000099}{y}-values that are valid for the function. ") → text10
  7. Segment(A, B) → a
  8. Segment(C, D) → b
  9. LaTeX((("\text{Domain=" * Constant) * "}")) → text15
  10. LaTeX((("\text{Range=" * sqrtx) * "}")) → text16
  11. LaTeX("\text{f(x)=\sqrt{x}}") → text14
  12. LaTeX("\text{f(x)=\sqrt{x}}") → FunctionText
  13. LaTeX("\text{x}") → text20
  14. LaTeX("\text{y}") → text21
  15. Segment(F, G) → c
  16. LaTeX((("\text{In this graph, the \textcolor{#000099}{y}-values start at \textcolor{#000099}{ y = " * sqrtx) * "} and continue to increase. ")) → text11
  17. Polygon(H, I, K, J) → poly1, h, i, k, j
  18. Intersect(h, i) → N
  19. Intersect(k, j) → O
  20. Polygon(L, M, N, O, R, S) → poly2, l, m, n, o, r, s
  21. LaTeX((("\text{The graph starts at \textcolor{#000099}{x = " * Constant) * "}, and continues infinitely in a positive}")) → text4
  22. LaTeX("\text{ direction. This means that only positive \textcolor{#000099}{x}-values are included in the") → text5
  23. LaTeX("\text{\mathbf{domain} the set of all input values (\textcolor{#000099}{x}-values) that satisfy the given function without}") → text1
  24. LaTeX("\text{restriction}") → text17
  25. LaTeX("\text{\mathbf{range} the set of all outputs of a function; the set of \textcolor{#000099}{y}-values that are valid for the}") → text18
  26. LaTeX("\text{function}") → text19
  27. LaTeX((("\text{equal to \textcolor{#000099}{" * Constant) * "}. }")) → text7
  28. LaTeX((("\text{Therefore, the domain is \textcolor{#000099}{\left\{ x ≥ " * Constant) * " \right\}}. }")) → text8
  29. LaTeX((("\text{Therefore, the range is all the numbers greater than or equal to \textcolor{#000099}{" * sqrtx) * "}.")) → text12
  30. LaTeX((("\text{The range is \textcolor{#000099}{\left\{ y ≥ " * sqrtx) * " \right\}}. }")) → text13