Limit comparisons (reviewing my Calc 1)

[rocomath]

So recently I been reviewing my graphing along with my Calculus 1.

I'm currently reading this problem and I was thinking, why not just compare it to a graph that I already know.

$$\lim_{x \rightarrow 5^{+}}\frac{6}{x-5}$$

with comparison to whose limit also goes to Infinity as it approaches from the right.

$$\lim_{x \rightarrow 0^{+}}\frac{1}{x}$$

Basically, my interpretation is that the first graph is simply stretched vertically by 6 and shifted 5 units from the graph of 1\x.

Is it ok for me to compare limits of similar functions such as the ones I just compared?

 

[Dick]

It's ok with me. Your description of the transformation from one to the other is correct. The sense in which these functions are 'similar' is that they are related by a change of variable.