Đồ thị hàm số \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiabg2 % da9maalaaabaGaaG4maiaadIhacqGHsislcaaIXaaabaGaaGOmaiaa % dIhacqGHRaWkcaaIXaaaaaaa!3EC0! y = \frac{{3x - 1}}{{2x + 1}}\) có tâm đối xứng là điểm.
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Lời giải:
Báo sai\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiqaaqaabe % qaamaaxababaGaciiBaiaacMgacaGGTbaaleaacaWG4bGaeyOKH46a % aeWaaeaacqGHsisldaWcaaqaaiaaigdaaeaacaaIYaaaaaGaayjkai % aawMcaamaaCaaameqabaGaey4kaScaaaWcbeaakiaadMhacqGH9aqp % cqGHsislcqGHEisPaeaadaWfqaqaaiGacYgacaGGPbGaaiyBaaWcba % GaamiEaiabgkziUoaabmaabaGaeyOeI0YaaSaaaeaacaaIXaaabaGa % aGOmaaaaaiaawIcacaGLPaaadaahaaadbeqaaiabgkHiTaaaaSqaba % GccaWG5bGaeyypa0Jaey4kaSIaeyOhIukaaiaawUhaaaaa!5603! \left\{ \begin{array}{l} \mathop {\lim }\limits_{x \to {{\left( { - \frac{1}{2}} \right)}^ + }} y = - \infty \\ \mathop {\lim }\limits_{x \to {{\left( { - \frac{1}{2}} \right)}^ - }} y = + \infty \end{array} \right.\) \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyO0H4Taam % iEaiabg2da9iabgkHiTmaalaaabaGaaGymaaqaaiaaikdaaaaaaa!3CC8! \Rightarrow x = - \frac{1}{2}\) là tiệm cận đứng của đồ thị hàm số.
\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci % GGSbGaaiyAaiaac2gaaSqaaiaadIhacqGHsgIRcqGHXcqScqGHEisP % aeqaaOGaamyEaiabg2da9maalaaabaGaaG4maaqaaiaaikdaaaaaaa!42DD! \mathop {\lim }\limits_{x \to \pm \infty } y = \frac{3}{2}\) nên \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiabg2 % da9maalaaabaGaaG4maaqaaiaaikdaaaaaaa!3981! y = \frac{3}{2}\) là tiệm cận ngang của đồ thị hàm số.
Vậy \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysamaabm % aabaGaeyOeI0YaaSaaaeaacaaIXaaabaGaaGOmaaaacaGG7aWaaSaa % aeaacaaIZaaabaGaaGOmaaaaaiaawIcacaGLPaaaaaa!3D07! I\left( { - \frac{1}{2};\frac{3}{2}} \right)\) là tâm đối xứng của đồ thị hàm số.