First, hook up you signal generator to an audio line amp input (below half a volt max) and sweep it from 5kHz to 20 kHz and listen to the sound.
If the output drops rapidly before 10kHz the generator might be defective. After that, as the frequency goes up to 10 kHz, its your ears, depending on your age.
Second, your provided no info on the oscilloscope. Even a real 1950 CRT scope will do better than that.
If it is a legit scope, it might be defective or have a blown input. Check 50 ohm vs 1 meg impedance on the scope that might load up a cheap generator?
Three, how is it connected (or badly connected) to the signal generator?