When a transmission is going bad it will often start slipping and hesitate to shift up properly.
If your transmission is not shifting your RPMS will go up but your vehicle will not pick up speed properly.
A properly working transmission should shift into the next gear within seconds of you pressing down on the accelerator pedal.
Other signs that your transmission may be going bad are.
Whining and Clunking noises, Lack of Response when accelerating, Burning Smell or Burnt Transmission Fluid, leaking Transmission Fluid, Transmission Grinding Gears, Noisy transmission in Neutral, Dashboard Lights including a check engine light.
A check engine light being on could also mean that your transmission is having problems.
Pull the transmission fluid dipstick and check the smell of the transmission fluid and if the transmission fluid is burnt you likely have some transmission problems.
Sometimes a transmission filter becomes clogged as well and results in the transmission not working.