Tangent Function Graph

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1. CSCA Math January 2026 Past Paper
   About the tangent function $y=\tan x$, which statement is correct?
   • A．The range is $[-1,1]$
   • B．The domain is $\mathbf{R}$
   • C．The function is even
   • D．The minimum positive period is $\pi$
   Antwort & Lösungsweg anzeigen

   Antwort: D

   Answer: D The domain of $y=\tan x$ is not all real numbers; $x=\frac{\pi}{2}+k\pi$ must be excluded. Its range is $\mathbf{R}$, it is odd, and its minimum positive period is $\pi$. Therefore D is correct.
   Die komplette CSCA Math January 2026 Past Paper bearbeiten – mit Zeit & Bewertung
2. CSCA Math March 2026 Past Paper
   Which description of $f ( x ) = \tan x$ is INCORRECT?
   • A．$f ( x )$ satisfies $f ( - x ) = - f ( x )$ on its domain
   • B．$f ( x )$ is an even function
   • C．$f ( x )$ is monotonically increasing on $( - \pi / 2 , \pi / 2 )$
   • D．$f ( x )$ has exactly one zero on ( $- \pi / 2 , \pi / 2$ )
   Antwort & Lösungsweg anzeigen

   Antwort: B

   tan $x$ is an odd function satisfying $f ( - x ) = - f ( x )$, not an even function. $C$ and $D$ correctly describe properties of $\tan \mathrm { x }$.
   Die komplette CSCA Math March 2026 Past Paper bearbeiten – mit Zeit & Bewertung
3. CSCA Math April 2026 Past Paper
   The minimum positive period of $y = 2 \tan \left( 3 x + \frac { \pi } { 4 } \right)$ is
   • A．$\frac { \pi } { 3 }$
   • B．$2 \pi$
   • C．$\frac { \pi } { 4 }$
   • D．$\pi$
   Antwort & Lösungsweg anzeigen

   Antwort: A

   For $\tan ( \omega x + \varphi )$, minimum positive period is $\frac { \pi } { | \omega | }$. Here $\omega = 3$, so $T = \frac { \pi } { 3 }$.
   Die komplette CSCA Math April 2026 Past Paper bearbeiten – mit Zeit & Bewertung