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．$y=\sin x$
   Lihat jawaban & pembahasan

   Jawaban: C

   Answer: C $y=2x+1$ is a linear function with positive slope, so it is increasing. Choose C.
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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．$y = - \frac { 1 } { x }$
   Lihat jawaban & pembahasan

   Jawaban: 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．$y = \cos x$
   Lihat jawaban & pembahasan

   Jawaban: 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).
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