Can a MOSFET be used to vary frequency in a function generator?

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lcr2139
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I am trying to build a function generator and I am unsure of how to build a circuit to vary frequency. Would I use a MOSFET? Can someone help me?
 
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Use a NE555 astable timer. See http://www.doctronics.co.uk/555.htm#astable . If you need to keep the same duty cycle as you vary the frequency, then varying the capacitor is best. If you want a 50% duty cycle, then divide the NE555 output by 2 with a 7474 D-type flip flop, which would then permit varying a resistor to vary frequency.
 
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There is an old function generator chip, called an Intersil ICL 8038. They are rare in Electronics stores, but Ebay sites have a few of them.

Here is a source of them:
http://www.ebay.com.au/itm/2PCS-IC-ICL8038CCPD-INTERSIL-DIP-14-/260968264013?pt=LH_DefaultDomain_0&hash=item3cc2ebb14d

These can provide sine, triangle and square wave output over the audio range and above.

Google for circuits of these chips.
Here is one:
http://www.eleccircuit.com/wp-content/uploads/2008/11/waveform-generator-with-icl8038.jpg

They are relatively simple to use but they need a power source with positive and negative voltages.

And you would need some way of calibrating it so that you would know what frequency was being generated. Look for a circuit with a digital display.
 
They also make direct digitial synthesization chips. I know maxim makes one. I think this method is filling the space where analog waveform chips have begun to be obsolete or at least to not be manufactured anymore.

http://en.wikipedia.org/wiki/Direct_digital_synthesizer

You would most likely want to use it with a microcontroller, since they can be configured over serial links like a uart, i2c, or spi.