Let $f : \mathbb{R} \to \mathbb{R}^3$ be defined by $f(t) = \left(3+8t, 6+9t, 3+6t\right)$.

(a) The graph of $f$ is a subset of $\mathbb{R}^k$ for $k =$ .
The image of $f$ is a subset of $\mathbb{R}^k$ for $k =$ .

(b) The graph of $f$ is the set $\Big\lbrace$ $\,\Big|\, t \in$ $\Big\rbrace.$

(c) The image of $f$ is the set $\Big\lbrace$ $\,\Big|\, t \in$ $\Big\rbrace.$