Nope, that's not an Emitter Follower (Google "Emitter Follower") circuit, and actually, that circuit is not biased correctly for class-A operation (more like class-C) -- unless the values you have chosen have to do with knowledge you have about the characteristics of the signal generator's output (since you do have it direct-coupled).
Disclaimer: I'm more of an MPU/digital guy, and I'm not as good with analog, but I'll give you what I've got:
As for constant 10V on the output of your amplifier, it might have to do with direct-coupling it to the signal generator output (because, otherwise, the way you have that transistor biased, I would expect it to be in "saturation" or "on" mode and the output to be near zero. But, if the signal generator's output impedance is 50ohm, then, that would explain the 10V output, as the low [50ohm] impedance would bias the transistor off.
I suggest using a capacitor between the sig. gen. output and your amp's input. For that frequency range, though, you need a large enough cap to pass the low frequencies, and yet you need to consider parasitic inductance which will limit it's ability to pass higher frequencies (not sure how to solve that, but perhaps with parallel caps, one a high value and one with a low value (and resonate frequency well above 10 MHz).
If you put a 3ohm resistor across the output of your sig gen and read 5V P-P across it (3.5V RMS), and it didn't get hot, it is either a VERY high wattage resistor (one that can dissipate around 4 watts [(5*.71)**2/3] and not get hot), or your testing device (not sure what a "CRO" is) is giving you an incorrect reading (it needs to be able to measure RMS at whatever frequency you have the sig gen set to). Try setting the sig gen to it's lowest freq setting. If the resistor is, indeed, 3 ohms, and there is 3.5 volts RMS across it, then it will dissipate around 4 watts -- that's the physics and nothing can change that. In other words, your statement "the signal generator only give me the signal but not a real voltage" is nonsensical. What?... as opposed to "imaginary voltage"?
When you measure the "signal" what are you using to measure it? If it's a scope, and that scope measures voltage in the time domain (or even frequency domain), then the voltage is there--the signal IS the voltage. So, something else must be wrong. I would suspect your instruments (broken or out of calibration) or an error in interpreting them. It's easy to be mislead by a reading, if you've made incorrect assumptions about the setup or device(s) that you are using to get that reading.
