Logarithmic Functions Graphing and Comparison

GeoGebra Commands & Parameters

1. Sequence(x = a, a, -7, -4, 0.5) → list1
2. LaTeX("\textcolor{#000099}{f(x)=-\log x}\text{ and }\textcolor{#000099}{g(x)=\log x}") → pair1
3. LaTeX("\textcolor{#000099}{h(x)=-\log_{2} {x}}\text{ and }\textcolor{#000099}{j(x)=\log_{2} {x}}") → pair2
4. LaTeX("\text{Three pairs of logarithmic functions are provided. Graph each pair on one coordinate}\cr\text{plane. Then, use the graphs to identify and compare the asymptotes, intercepts,}\cr \text{domains, and ranges for each pair, as well as the shape and end behavior of each pair}\cr \text{of graphs.}") → problemtext
5. LaTeX("\textcolor{#000099}{m(x)=-\ln x}\text{ and }\textcolor{#000099}{p(x)=\ln x}") → pair3
6. TableText({{pair1}, {pair2}, {pair3}}, "l") → text1
7. LaTeX("\text{Graph the first pair of functions on the same coordinate plane.}") → text2
8. LaTeX("\textcolor{#FF0000}{f(x)=-\log x}") → ftext
9. LaTeX("\textcolor{#006400}{g(x)=\log x}") → gtext
10. LaTeX("\text{Compare the shapes and end behavior of the graphs.}") → text3
11. LaTeX("\text{The line of reflection is the }\textcolor{#FF00FF}\text{x-axis}\text{.}") → text4
12. LaTeX((((("\text{The shape and end behavior of the graph of }\textcolor{#FF0000}{" * ftext) * "}\text{ are inverted}\cr \text{from the shape and end behavior of the graph of }\textcolor{#006400}{") * gtext) * "}\text{. In}\cr \text{other words, the two graphs are reflections of each other.} ")) → text33
13. LaTeX((((("\text{The graph of }\textcolor{#FF0000}{" * ftext) * "}\text{ decreases as }\textcolor{#000099}\text{x}\text{ approaches positive infinity.}\cr \text{The graph of }\textcolor{#006400}{") * gtext) * "}\text{ increases as }\textcolor{#000099}\text{x}\text{ approaches positive infinity.}")) → text5
14. LaTeX("\text{Identify the two graphs’ asymptotes, intercepts, domains, and ranges.}") → text6
15. LaTeX("\text{Since neither graph crosses the }\textcolor{#000099}\text{y-axis}\text{, both graphs have a vertical}\cr\text{asymptote at }\textcolor{#FF00FF}\text{x = 0}\text{.}") → text7
16. LaTeX("\text{The graphs cross the }\textcolor{#000099}\text{x-axis}\text{ at the x-intercept }\textcolor{#000099}{\left(1, 0 \right)}\text{.}") → text8
17. LaTeX("\text{Since the }\textcolor{#000099}{x-values}\text{ increase into positive infinity but never cross the}\cr\textcolor{#000099}{y-axis}\text{, this means they are never negative. Thus, we can determine the}\cr\text{domain of both graphs is }\textcolor{#000099}{x > 0}\text{.}") → text9
18. Ray((0.1, 0), (1, 0)) → c
19. LaTeX("\text{The range of both graphs is }{\textcolor{#000099}\text{all real numbers}\text{.}") → text10
20. LaTeX("\text{Graph the second pair of functions together on a new coordinate plane.}") → text11
21. LaTeX("\textcolor{#006400}{j(x)=\log_{2}{x}}") → jtext
22. LaTeX("\textcolor{#FF0000}{h(x)=-\log_{2}{x}}") → htext
23. LaTeX((((("\text{The graph of }\textcolor{#006400}{" * jtext) * "}\text{ and }\textcolor{#FF0000}{") * htext) * "}\text{ is shown.}")) → text111
24. LaTeX("\text{Compare the shapes and end behavior of the second pair of graphs.}") → text12
25. LaTeX((((("\text{The shape and end behavior of the graph of }{" * htext) * "}\text{ are inverted}\cr\text{from that of }{") * jtext) * "}\text{. In other words, each graph is a reflection of}\cr\text{the other over the }\textcolor{#FF00FF}\text{x-axis}\text{.}")) → text122
26. LaTeX((((("\text{The graph of }{" * htext) * "}\text{ decreases as }\textcolor{#000099}\text{x}\text{ approaches positive infinity.}\cr \text{The graph of }{") * jtext) * "}\text{ increases as }\textcolor{#000099}\text{x}\text{ approaches positive infinity.}")) → text13
27. LaTeX("\text{Identify the two graphs’ asymptotes, intercepts, domains, and ranges.}") → text14
28. LaTeX("\text{There is a vertical asymptote at }{\textcolor{#FF00FF}\text{x = 0}\text{ for each graph.}") → text15
29. LaTeX("\text{Both graphs cross the }\textcolor{#000099}\text{x-axis}\text{ at the x-intercept }\textcolor{#000099}{\left(1, 0\right)}\text{.}") → text16
30. LaTeX("\text{The domain of both graphs is }\textcolor{#000099}\text{x > 0}\text{.}") → text17
31. LaTeX("\text{Since the y-values are not limited, we can determine the range of each graph}\cr\text{is }\textcolor{#000099}\text{all real numbers}\text{.}") → text18
32. LaTeX("\text{Graph the third pair of functions together on a new coordinate plane.}\cr \text{Compare the graphs’ shapes and end behavior.}") → text19
33. LaTeX("\textcolor{#006400}{p(x)=\ln x}") → ptext
34. LaTeX("\textcolor{#FF0000}{m(x)=-\ln x}") → mtext
35. LaTeX((((("\text{The graph of }{" * ptext) * "}\text{ and }{") * mtext) * "}\text{ is shown.}")) → text20
36. LaTeX((((("\text{The shape and end behavior of the graph of }{" * mtext) * "}\text{ are inverted}\cr \text{from that of }{") * ptext) * "}\text{; therefore, the graphs are reflections of one}\cr\text{another. The line of reflection is the }\textcolor{#FF00FF}\text{x-axis}\text{.}")) → text21
37. LaTeX((((("\text{The graph of }{" * mtext) * "}\text{ decreases as }\textcolor{#000099}\text{x}\text{ approaches positive infinity.}\cr\text{The graph of }{") * ptext) * "}\text{ increases as }\textcolor{#000099}\text{x}\text{ approaches positive infinity.}")) → text22
38. LaTeX((((("\text{Graph the given functions, }{" * ftext) * "}\text{ and }{") * gtext) * "}\text{, by hand or}\cr\text{using a graphing calculator. The result should resemble the following.}")) → textnew2
39. LaTeX("\text{Use the graphs to identify the asymptotes, intercepts, domains, and}\cr \text{ranges of this third pair of functions.}") → text23
40. LaTeX("\text{There is a vertical asymptote at }\textcolor{#FF00FF}\text{x = 0}\text{.}") → text24
41. LaTeX("\text{The graphs cross the x-axis at the x-intercept }\textcolor{#000099}{\left(1, 0\right)}\text{.}") → text25
42. LaTeX("\text{The domain of both graphs is }\textcolor{#000099}\text{x > 0}\text{.}") → text26
43. LaTeX("\text{The range of both graphs is }\textcolor{#000099}\text{all real numbers}\text{.}") → text27
44. LaTeX("\text{Summarize your findings.}") → text28
45. LaTeX("\text{In summary, all three pairs of graphs have the same vertical asymptote}\cr\text{of }\textcolor{#FF00FF}\text{x = 0}\text{. In every case, the x-intercept is }\textcolor{#000099}{\left(1, 0\right)}\text{. The domain and range}\cr \text{for all three pairs are identical. The three pairs of functions}\cr\text{differ in the rate of increase or decrease as }\textcolor{#000099}\text{x}\text{ increases.}") → text29
46. Text("Move the slider to solve the problem.") → text0