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]
What is the relationship between the pair of graphs [math]y=f\left(x\right)[/math] and [math]y=f_1\left(x\right)[/math]?
What is the relationship between the pair of graphs [math]y=g\left(x\right)[/math] and [math]y=g_1\left(x\right)[/math]?
What is the relationship between the pair of graphs [math]y=h\left(x\right)[/math] and [math]y=h_1\left(x\right)[/math]?
Can you make a general conjecture about the relationship between the graphs of [math]y=F\left(x\right)[/math] and [math]y=F\left(x\right)+a[/math] from your observations about the graphs of the pairs of functions above?