Let $G$ be the affine group of order $1$ over $\mathbb{R}$, i.e., $G$ is the set of functions
$$T_{a,b}: \mathbb{R} \rightarrow \mathbb{R}, \ T_{a,b} (x) = ax + b$$
Where $a, b \in \mathbb{R}$ and $a \neq 0$ and the group operation given by the composition of functions.
We defined several subsets of G:
$$ \begin{align} N &= \big \{ T_{1,b} \in G \mid b \in \mathbb{R} \big\} \\ A &= \big \{ T_{a,0} \in G \mid a \in \mathbb{R}, a \neq 0 \big \} \\ H &= \big \{ T_{1,b} \in G \mid b \in \mathbb{Z} \big \} \end{align} $$
I want to approach this question using sagemath 9.4 but running into issues.
G = AffineGroup(1, RR)
The above code snippet is what I'm using to as a start. However, documentation on working with the group with that degree isn't helpful. But I am curious if there is a way to access the elements of the group and manipulate them.