Question

the function f is defined as follows.

\\f(x) = \

$$\begin{cases} 2x & \\text{if } x \ eq 0 \\\\ 4 & \\text{if } x = 0 \\end{cases}$$

\\

(a) find the domain of the function.
(b) locate any intercepts.
(c) graph the function.
(d) based on the graph, find the range.

part 1 of 4

(a) the domain of the function f is box.
(type your answer in interval notation.)

Explanation:

Analyze the piecewise domains

$$ \text{Domain}_1 = \{x \in \mathbb{R} \mid x eq 0\} = (-\infty, 0) \cup (0, \infty) $$

$$ \text{Domain}_2 = \{0\} $$

Combine the sub-domains

$$ \text{Domain} = \text{Domain}_1 \cup \text{Domain}_2 = (-\infty, 0) \cup \{0\} \cup (0, \infty) = (-\infty, \infty) $$

Answer:

(a) The domain of the function f is <blank>\((-\infty, \infty)\)</blank>.