taiwan-gsat 2025 Q8

taiwan-gsat · Other · gsat__math-b 5 marks Curve Sketching Multi-Statement Verification (Remarks/Options)
Let $\Gamma$ be the graph of the function $y = x ^ { 3 } - x$ on the coordinate plane. Select the correct options.
(1) The center of symmetry of $\Gamma$ is the origin
(2) $\Gamma$ approximates the line $y = x$ near $x = 0$
(3) $\Gamma$ can coincide with the graph of the function $y = x ^ { 3 } + x + 3$ after appropriate translation
(4) $\Gamma$ and the graph of the function $y = x ^ { 3 } + x$ are symmetric about the $x$-axis
(5) $\Gamma$ and the graph of the function $y = - x ^ { 3 } + x$ are symmetric about the $y$-axis
Let $\Gamma$ be the graph of the function $y = x ^ { 3 } - x$ on the coordinate plane. Select the correct options.\\
(1) The center of symmetry of $\Gamma$ is the origin\\
(2) $\Gamma$ approximates the line $y = x$ near $x = 0$\\
(3) $\Gamma$ can coincide with the graph of the function $y = x ^ { 3 } + x + 3$ after appropriate translation\\
(4) $\Gamma$ and the graph of the function $y = x ^ { 3 } + x$ are symmetric about the $x$-axis\\
(5) $\Gamma$ and the graph of the function $y = - x ^ { 3 } + x$ are symmetric about the $y$-axis