Determine Whether the Graph Is That of a Function $\{x \mid-\pi \leq x \leq \pi\}$

question 17

Multiple Choice

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if
any, and any symmetry with respect to the x-axis, the y-axis, or the origin.
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• A) function domain: \( \{x \mid-\pi \leq x \leq \pi\} \) range: \( \{y \mid-1 \leq y \leq 1\} \) intercepts: \( (-\pi, 0),(0,0),(\pi, 0) \) symmetry: origin
• B) function domain: all real numbers range: \( \{\mathrm{y} \mid-1 \leq \mathrm{y} \leq 1\} \) intercepts: \( (-\pi, 0),(0,0),(\pi, 0) \) symmetry: origin
• C) function domain: \( \{x \mid-1 \leq x \leq 1\} \) range: \( \{y \mid-\pi \leq y \leq \pi\} \) intercepts: \( (-\pi, 0),(0,0),(\pi, 0) \) symmetry: none
• D) \(\text { not a function }\)

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Definitions:

Noam Chomsky

An American linguist, philosopher, cognitive scientist, historian, social critic, and political activist known for his theory of generative grammar.

Biological Propensity

Biological propensity involves the natural inclination or tendency within individuals due to genetic, hormonal, or neurophysiological factors to exhibit certain behaviors or to develop certain conditions.

Linguistic Relativity

The hypothesis that the structure of a language influences its speakers' world view or cognition.

Nativist

A perspective in psychology and linguistics suggesting that certain skills or abilities are "native" or hardwired into the brain at birth, contrasting with theories that emphasize learning and experience.