Exponents and Exponential Functions

실제 시험에서는 이렇게 출제됩니다

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

1. CSCA Math December 2025 Past Paper
   Which statement about $y=\left(\frac{1}{2}\right)^x$ is correct?
   • A．It is increasing.
   • B．It is decreasing.
   • C．It is symmetric about the origin.
   • D．It is symmetric about the $x$-axis.
   정답 및 풀이 보기

   정답: B

   Answer: B The base $\frac{1}{2}$ is between 0 and 1, so the exponential function is decreasing. Choose B.
   CSCA Math December 2025 Past Paper 전체에서 보기
2. CSCA Math January 2026 Past Paper
   About the exponential function $y=a^x$ ($a>0$, $a\neq1$), which statement is incorrect?
   • A．The range is $(0,+\infty)$
   • B．The graph passes through $(0,1)$
   • C．The function is increasing on its domain
   • D．The domain is $\mathbf{R}$
   정답 및 풀이 보기

   정답: C

   Answer: C For $y=a^x$, the domain is $\mathbf{R}$, the range is $(0,+\infty)$, and the graph passes through $(0,1)$. It is increasing only when $a>1$ and decreasing when $0<a<1$, so statement C is not always true.
   CSCA Math January 2026 Past Paper 전체 풀기 — 시간 측정 및 채점
3. CSCA Math April 2026 Past Paper
   Function $y = a ^ { x }$ is decreasing on $\mathbb { R }$ when
   • A．$a > 0$
   • B．$0 < a < 1$
   • C．$a > 1$
   • D．$a < 1$
   정답 및 풀이 보기

   정답: B

   Exponential $a ^ { x }$ (with $a > 0 , a \neq 1$ ) is decreasing iff $0 < a < 1$.
   CSCA Math April 2026 Past Paper 전체 풀기 — 시간 측정 및 채점