Function Monotonicity

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이 개념을 다룬 실제 CSCA 기출문제입니다. 답을 펼치기 전에 먼저 직접 풀어 보세요.

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．$y=\sin x$
   정답 및 풀이 보기

   정답: C

   Answer: C $y=2x+1$ is a linear function with positive slope, so it is increasing. Choose C.
   CSCA Math December 2025 Past Paper 전체에서 보기
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．$y = - \frac { 1 } { x }$
   정답 및 풀이 보기

   정답: 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 $y ^ { \prime } = \frac { 1 } { x ^ { 2 } } > 0$.
   CSCA Math April 2026 Past Paper 전체 풀기 — 시간 측정 및 채점
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．$y = \cos x$
   정답 및 풀이 보기

   정답: 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).
   CSCA Math June 2026 Past Paper 전체 풀기 — 시간 측정 및 채점