Function Monotonicity

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1. CSCA Math December 2025 Past Paper
   Which of the following functions is increasing?
   • A．$y=\log_{0.5}x$
   • B．$y=\left(\frac{1}{3}\right)^x$
   • C．$y=2x+1$
   • D．$y=\sin x$
   Antwort & Lösungsweg anzeigen

   Antwort: C

   Answer: C $y=2x+1$ is a linear function with positive slope, so it is increasing. Choose C.
   In der vollständigen CSCA Math December 2025 Past Paper ansehen
2. CSCA Math April 2026 Past Paper
   Which function is decreasing on $( - \infty , + \infty )$ ?
   • A．$y = - x + 5$
   • B．$y = x ^ { 3 }$
   • C．$y = x ^ { 2 } + 1$
   • D．$y = - \frac { 1 } { x }$
   Antwort & Lösungsweg anzeigen

   Antwort: A

   (A) Linear with slope $- 1 < 0$, decreasing on all of $\mathbb { R } \checkmark$. (B) $x ^ { 3 }$ is increasing on $\mathbb { R }$; (C) parabola is not monotonic; (D) undefined at $x = 0$, so not on all of $\mathbb { R }$; moreover on each piece $( - \infty , 0 )$ and $( 0 , + \infty )$ it is in fact increasing, since $y ^ { \prime } = \frac { 1 } { x ^ { 2 } } > 0$.
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3. CSCA Math June 2026 Past Paper
   Which of the following functions is monotonically decreasing?
   • A．$y = e^{-x}$
   • B．$y = x^2 - 1$
   • C．$y = 100^x$
   • D．$y = \cos x$
   Antwort & Lösungsweg anzeigen

   Antwort: A

   $y = e^{-x} = \left( \frac{1}{e} \right)^x$ with base $\frac{1}{e} < 1$ is monotonically decreasing, so (A) is correct. $y = x^2 - 1$ decreases on $(-\infty, 0)$ and increases on $(0, +\infty)$, so it is not monotonic; $y = 100^x$ has base greater than 1 and is increasing; $y = \cos x$ is periodic and not monotonic on its domain. Choose (A).
   Die komplette CSCA Math June 2026 Past Paper bearbeiten – mit Zeit & Bewertung