When 'h' increases in a rational function, what happens to the function?

In the context of rational functions, when 'h' increases, it typically refers to a horizontal shift in the graph of the function. This means the entire graph of the rational function will move to the right along the x-axis.

For example, if you have a function like f(x) = 1/(x - h), when you increase 'h', the term (x - h) means that the function will be evaluated at larger values of x to yield the same output. As such, the input at which the function reaches its vertical asymptote also shifts rightward, indicating a shift of the whole function.

This deliberate manipulation of 'h' changes the horizontal position of the graph, emphasizing the direct relationship between 'h' and the left-right positioning of the rational function on the coordinate plane. Hence, increasing 'h' corresponds accurately with the movement of the function rightward.