I agree it could be a slipping clutch , . Try driving off with the handbrake on hard. The car should stall . (assuming the handbrake is good - the Jazz has a bit of a reputation for sometimes having a fairly weak handbrake. )
If engine speed rises and the car isnt moving as it should the clutch may be worn out ,or contaminated with oil,and need replacing. ( Good workshop practice is to replace the oil seal anyway when changing the clutch whether it leaking or not ,so cost should be the same. ) But get expert opinion before spending cash.
If its a cvt automatic, I dont know much about these. With these some mismatch between engine and road speed is normal. But if its worse than usual it might also be the source of similar problems.