Let $f : \mathbb{R} \to \mathbb{R}$ be defined by $f(x) = 2\cos\!\left(x\right)$ and set $y = f(x)$.

(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 $\Big\lbrace$ $\,\Big|\, x \in$ $\Big\rbrace.$

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

(d) Choose which is the graph of $f$ and which is the image of $f$ below.
Figure A is the Choose Graph of f Image of f and figure B is the Choose Graph of f Image of f .