Trace the graph of [math]f_1(x)=x^3[/math] by changing the values in the slider [math]a[/math]. What is the natural domain of [math]f_1(x)[/math]? Use the slider [math]b[/math] to trace the graph of [math]f_2(x)=-x^3[/math].

Trace the graph of [math][math]g_1(x)=\frac{1}{x^2}[/math][/math] by changing the values in the slider [math]a[/math]. What is the natural domain of [math]g_1(x)[/math]? Use the slider [math]b[/math] to trace the graph of [math][math]g_2(x)=-\frac{1}{x^2}[/math][/math].

Trace the graph of [math]h_1(x)=3^x[/math] by changing the values in the slider [math]a[/math]. What is the natural domain of [math]h_1(x)[/math]? Use the slider [math]b[/math] to trace the graph of [math]h_2(x)=-3^x[/math].

What is the relationship between the functions in the pairs [math]f_1[/math] and [math]f_2[/math]; [math]g_1[/math] and [math]g_2[/math]; [math]h_1[/math] and [math]h_2[/math]?[br][br]Can you make a general conjecture regarding the graphs of functions from your observations of the graphs of these pairs?