Speed of Functions Approaching Infinity

Here I wanted to produce a visual representation of the fact that different well known functions approach infinity faster than others and explore the order of the speed at which they do. My main application for this has been when wanting to identify the dominant term of a sequence whose general term is a quotient, as a means to finding it's limit, if it exists. I am usually least clear on functions in the form of h(x) and a(x) but straight away I can see from this graph that a(x) approaches infinity faster as x increases so this visual aid will help me remember this!