Question

suppose the graph of the parent function $y = \cot(x)$ is vertically compressed to produce the graph of the function $y = a\cot(x)$, but there are no reflections. which describes the value of $a$?
\\(\bigcirc\\) $a < -1$
\\(\bigcirc\\) $-1 < a < 0$
\\(\bigcirc\\) $0 < a < 1$
\\(\bigcirc\\) $a > 1$

Explanation:

Step1: Recall Vertical Compression Rules

For a function \( y = a \cdot f(x) \), vertical compression occurs when \( 0 < |a| < 1 \). Since there are no reflections, \( a \) must be positive (reflection would be \( a < 0 \)).

Step2: Analyze the Sign and Magnitude of \( a \)

Given no reflections, \( a>0 \). For vertical compression, \( |a| < 1 \). Combining these, \( 0 < a < 1 \).

Answer:

\( 0 < a < 1 \) (corresponding to the option "0 < a < 1")