Chapter Implicit Function Graphs You can graph any one of the following types of implicit functions using the calculator’s built-in functions.
14-1 Before Graphing an Implicit Function k Entering the CONICS Mode 1. In the Main Menu, select the CONICS icon and enter the CONICS Mode. When you do, the following built in function menu appears on the screen. 2. Use f and c to highlight the built-in function you want, and then press w. The following nine functions are built in.
14-2 Graphing an Implicit Function Example 1 To graph the circle (X – 1)2 + (Y – 1)2 = 22 Use the following View Window parameters. Xmin = –6.3 Ymin = –3.1 Xmax = 6.3 Ymax = 3.1 Xscale = 1 Yscale = 1 1. Select the function whose graph you want to draw. cccc 2. Press w and the variable input screen appears. Graph function Function variables • The values that appear are the values currently assigned to each variable, which are general variables used by the calculator.
14 - 2 Graphing an Implicit Function Example 2 (X – 3)2 (Y – 1)2 To graph the hyperbola –––––––––– – –––––––––– =1 2 22 2 Use the following View Window parameters. Xmin = –8 Ymin = –10 Xmax = 12 Ymax = 10 Xscale = 1 Yscale = 1 1. Select the function whose graph you want to draw. ccccccc 2. Press w and the variable input screen appears. 3. Assign values to each variable. cwcwdwbw 4. Press 6 (DRAW) to draw the graph.
Graphing an Implicit Function 14 - 2 • Implicit function graphs can be drawn in blue only. • You cannot overwrite implicit function graphs. • The calculator automatically clears the screen before drawing a new implicit function graph. • You can use trace, scroll, zoom, or sketch after graphing an implicit function. However, an implicit function graph cannot be scrolled while using trace. • You cannot incorporate graphing of an implicit function into a program.
14 - 2 Graphing an Implicit Function • A hyperbola is the locus of points related to two given points F and F’ such that the difference in distances of each point from the two given points is constant.
14-3 Implicit Function Graph Analysis You can determine approximations of the following analytical results using implicit function graphs. • Focus/vertex calculation • Latus rectum calculation • Center/radius calculation • x-/y-intercept calculation • Directrix/axis of symmetry drawing and analysis • Asymptote drawing and analysis After graphing an implicit function, press 5 (G-Solv) to display the Graph Analysis Menu. Parabolic Graph Analysis • {FOCS} ... {determines the focus} • {SYM}/{DIR} ...
14 - 3 Implicit Function Graph Analysis 5 (G-Solv) 1 (FOCS) (Calculates the focus.) 5 (G-Solv) 4 (VTX) (Calculates the vertex.) • When calculating two foci for an ellipse or hyperbolic graph, press e to calculate the second focus. Pressing d returns to the first focus. • When calculating two vertexes for a hyperbolic graph, press e to calculate the second vertex. Pressing d returns to the first vertex.
Implicit Function Graph Analysis 14 - 3 5 (G-Solv) 1 (CNTR) (Calculates the center.) 5 (G-Solv) 2 (RADS) (Calculates the radius.) u To calculate the x- and y-intercepts Example [G-Solv]-[X-IN]/[Y-IN] To determine the x- and y-intercepts for the hyperbola (X – 1)2 (Y – 1)2 –––––––––– – –––––––––– = 1 22 22 Use the following View Window parameters. Xmin = –6.3 Ymin = –3.1 Xmax = 6.3 Ymax = 3.1 Xscale = 1 Yscale = 1 5 (G-Solv) 2 (X-IN) (Calculates the x-intercept.
14 - 3 Implicit Function Graph Analysis u To draw and analyze the axis of symmetry and directrix [G-Solv]-[SYM]/[DIR] Example To draw the axis of symmetry and directrix for the parabola X = 2(Y – 1)2 + 1 Use the following View Window parameters. Xmin = –6.3 Ymin = –3.1 Xmax = 6.3 Ymax = 3.1 Xscale = 1 Yscale = 1 5 (G-Solv) 2 (SYM) (Draws the axis of symmetry.) 5 (G-Solv) 3 (DIR) (Draws the directrix.
Implicit Function Graph Analysis 14 - 3 • Certain View Window parameters can produce errors in values produced as graph analysis result. • The message ”Not Found” appears on the display when graph analysis is unable to produce a result. • The following can result in inaccurate analysis results or may even make it impossible to obtain a solution at all. — When the solution is tangent to the x-axis. — When the solution is a point of tangency between two graphs.
