Use the slider on each graph to change the values of [math]a[/math] in the functions [math]f(x)=x^3+a[/math], [math]g(x)=\frac{1}{x^2}+a[/math], and [math]h(x)=3^x+a[/math]. [br][br]Is there any relationship between the pairs of graphs ([math]f(x)[/math] and[math]f_1\left(x\right)[/math]; [math]g(x)[/math] and [math]g_1\left(x\right)[/math]; [math]h(x)[/math] and [math]h_1\left(x\right)[/math])?

Can you make a general conjecture about the graphs of functions from your observations of the graphs of these pairs?