taiwan-gsat 2023 Q12

taiwan-gsat · Other · gsat__math-a 5 marks Trig Graphs & Exact Values
Let $f(x) = \sin x + \sqrt{3} \cos x$. Select the correct options.
(1) The vertical line $x = \frac{\pi}{6}$ is an axis of symmetry of the graph of $y = f(x)$
(2) If the vertical lines $x = a$ and $x = b$ are both axes of symmetry of the graph of $y = f(x)$, then $f(a) = f(b)$
(3) In the interval $[0, 2\pi)$, there is only one real number $x$ satisfying $f(x) = \sqrt{3}$
(4) In the interval $[0, 2\pi)$, the sum of all real numbers $x$ satisfying $f(x) = \frac{1}{2}$ does not exceed $2\pi$
(5) The graph of $y = f(x)$ can be obtained from the graph of $y = 4\sin^{2}\frac{x}{2}$ by appropriate (left-right, up-down) translation
Let $f(x) = \sin x + \sqrt{3} \cos x$. Select the correct options.\\
(1) The vertical line $x = \frac{\pi}{6}$ is an axis of symmetry of the graph of $y = f(x)$\\
(2) If the vertical lines $x = a$ and $x = b$ are both axes of symmetry of the graph of $y = f(x)$, then $f(a) = f(b)$\\
(3) In the interval $[0, 2\pi)$, there is only one real number $x$ satisfying $f(x) = \sqrt{3}$\\
(4) In the interval $[0, 2\pi)$, the sum of all real numbers $x$ satisfying $f(x) = \frac{1}{2}$ does not exceed $2\pi$\\
(5) The graph of $y = f(x)$ can be obtained from the graph of $y = 4\sin^{2}\frac{x}{2}$ by appropriate (left-right, up-down) translation