Graph Transformations: y=F(x)+a

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]

Task 1

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] below?

y=f(x)

Task 2

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] below?

y=g(x)

Task 3

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] below?

y=h(x)

Task 4

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?