Below is the graph of [math]g\left(x\right)=a\cdot\frac{1}{x^2}[/math], where a is the value in the slider. Change the values of a and check what happens to the graph of f(x). [br]What is the domain of g(x)? What is the relationship between the graphs of [math]g\left(x\right)=\frac{1}{x^2}[/math] and [math]g\left(x\right)=-\frac{1}{x^2}[/math]?

Change the values of [math]a[/math] to alter the graph of [math]h(x)=a\cdot3^x[/math]. What is the natural domain of [math]h(x)[/math]? What is the relationship between the graphs of [math]h(x)=3^x[/math] and [math]h(x)=-3^x[/math]?

Below is the graph of [math]f(x)=a\cdot x^3[/math], what happens to the graph of f(x) as a changes?[br][br]What is the relationship between the graph of [math]f(x)=-x^3[/math] and [math]f(x)=x^3[/math]?

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