综合几何与函数图像示例：多边形、参数曲线与体积计算

GeoGebra 命令及参数

1. Point(p_1) → P_1
2. Point(xAxis) → B
3. Segment(W, Z) → p
4. Intersect(xAxis, yAxis) → D_1
5. Point(yAxis) → E_1
6. Vector(D_1, E_1) → w
7. Point(xAxis) → F_1
8. Vector(D_1, F_1) → u_1
9. Point(yAxis) → G_1
10. Vector(D_1, G_1) → v_1
11. Point(xAxis) → H_1
12. Vector(D_1, H_1) → w_1
13. LaTeX("\text{Identify the type of function.}") → text1_2
14. LaTeX((("\text{Step {" * Slider) * "} of 5}")) → text1_5
15. LaTeX("\text{\mathbf{Note}\mathbf{:} Use the (Data Kit) \\to return to the original \\problem or randomly generate \\a similar practice problem.\\Use the (Definition) to \\review words to know.}") → text2
16. LaTeX("\text{Click the button to solve the problem.}") → text8
17. LaTeX("\text{Draw the asymptote and the two given points on a coordinate plane.}") → text1_3
18. Point(h_1) → J_1
19. Point(h_1) → K_1
20. Segment(J_1, K_1) → f
21. Point(i_1) → L_1
22. Point(i_1) → M_1
23. Segment(L_1, M_1) → asymptote
24. LaTeX((((((("\text{Identify the type of function that has an asymptote at \textcolor{#000099}{\mathit{y}={" * as) * "}},has\\a \textcolor{#000099}{\mathit{y}}-intercept at \textcolor{#000099}{(0, {") * y1) * "})},is decreasing for all \textcolor{#000099}{\mathit{x}}-values,and goes\\through the point \textcolor{#000099}{(1,{") * y2) * "})}.Then,draw a graph of the function.}")) → text1
25. LaTeX("\text{Because there is an asymptote and a \textcolor{#000099}{\mathit{y}}-intercept,the function\\is exponential.}") → text1_1
26. LaTeX((("\text{Asymptote at \textcolor{#000099}{\mathit{y}={" * as) * "}}")) → text3
27. LaTeX("\text{\mathit{x}}") → text7
28. LaTeX("\text{\mathit{y}}") → text7_1
29. LaTeX("\text{\mathbf{Asymptote:} An asymptote is a value that you get closer and closer to,but\\ never quite reach.}") → text6
30. LaTeX((("\text{\mathit{y}-intercepts:\textcolor{#000099}{(0,{" * y1) * "})}")) → text4
31. LaTeX((("\text{Point goes through:\textcolor{#000099}{(0,{" * y2) * "})}")) → text5
32. Polygon(N, Z_1, I_2, J_2, A_2, B_2, C_2, D_2, E_2, F_2, G_2, H_2) → poly1, n, h_2, i_2, j_2, z_1, a_2, b_2, c_2, d_2, e_2, f_2, g_2
33. Point(n) → P_2
34. Point(b_2) → S_2
35. Polygon(K_2, L_2, M_2, N_2, O_2, P_2, Q_2, R_2, S_2) → poly2, k_2, l_2, m_2, n_2, o_2, p_2, q_2, r_2, s_2
36. Intersect(a_2, b_2) → W_2
37. Point(r_2) → Z_2
38. Polygon(T_2, U_2, N_2, V_2, W_2, Z_2) → poly3, t_2, u_2, n_1, v_2, w_2, z_2
39. LaTeX("\text{\mathbf{Point :} A point on the coordinate plane is a location defined by an \\ ordered pair of the form (x,y).}") → text6_1
40. LaTeX("\text{Graph the given key features.}") → text1_4
41. LaTeX("\text{Graph the function. \\Because the function is decreasing and can’t go beyond the asymptote,\\we can roughly draw in the curve required.}") → text1_6