An increase in 'a' in a rational function affects the function how?

In a rational function of the form ( f(x) = \frac{a}{g(x)} ), where ( g(x) ) is a polynomial or another function of ( x ), an increase in the parameter ( a ) directly influences the height of the graph. Specifically, increasing ( a ) scales the function vertically. This means that for any given value of ( x ), the output ( f(x) ) will be larger when ( a ) is increased, making the function stretch outward from the x-axis.

This scaling leads to a steeper rise or fall in the graph, depending on the nature of ( g(x) ). If ( a ) is positive, an increase will move the function upward, while if ( a ) is negative, it will move it further downward. The change does not translate into horizontal shifts or movements left or right since those would require changes in the function's denominator or independent variable. Thus, the correct understanding is that increasing 'a' in a rational function results in the function moving outward, effectively scaling its values depending on the context around each specific x-value.