Final answer:
Graphing a function of three variables often requires the use of 3D graphing tools, statistical software, or advanced calculators like TI-83/84 series. Equation graphers aid in visualizing polynomial curves by adjusting constants. Ternary plots or 3D graphing software can be used depending on the function's form.
Step-by-step explanation:
Graphing a function of three variables can be a challenging task because it requires a 3D representation. Most online graphing calculators are equipped to handle functions of two variables, like y = f(x), but graphing in three dimensions involves an additional variable, such as z = f(x, y). Equation graphers and more sophisticated software such as statistical tools or computer spreadsheets can simplify the process.
One way to visualize three-variable functions is through ternary plots, which are used to depict the ratios of the three variables as positions within an equilateral triangle. However, for functions that cannot be expressed in terms of ratios, 3D graphing software or calculators like the TI-83, TI-83+, and TI-84+ would be more appropriate. These calculators can help find the best-fit line for data points and create scatter plots, which is helpful in understanding the relationship between variables.
When graphing polynomials, equation graphers often provide interactive experiences where the change in the constants alters the shape of the curve. This allows students to see how individual terms like y = bx contribute to the overall polynomial curve. For instance, to graph a best-fit line on a TI calculator, one would input the linear equation into the Y= menu and use graphing features to visualize it.