Water at my house cuts in and out when I turn it on.

Are you on a well or city water system? If you are on a well watch your pressure gauge when the water is running and get back to us with more info

If you're on a well, take a look at your pressure tank. It probably has a little air valve at the top somewhat like the air valve on a car tire. Depress the valve for few seconds and see if you get water or air. If it's water, then you need a new tank.

Your bladder tank's water logged.
Let me explain the function of a bladder tank. Pressure and bladder tanks provide a air cushion that produces water pressure in your system so your pump doesn't kick on every time you draw a glass of water. A bladder tank has a neoprene membrane in the center. As the pump puts water into the bottom half of the bladder tank the membrane compresses the air in the top half. When the pressure reaches the cut off point in the control box the pump shuts down. However you still have between 40 to 50 pounds of pressure pushing the water out to your system. As the pressure drops in the tank when you make a draw the pump kicks on and everything starts over again.
To check, take something metal and start rapping at the bottom of the tank and work upwards. You will hear a "clunk" in the bottom half full of water. On the upper half you should hear a "clink" because the upper half should have nothing but air in it. IF the sound doesn't change or changes close to to tank top then the bladder tank must be replaced. Your air setting on the tank should be 2 pounds UNDER the cut in point in the pressure control box. If your pressure control has a 20 PSI cut in and 40 PSI cut out the tank pressure should read 18 PSI. The bladder tank setting MUST be made with the pump off and the system bled down by opening a cold water faucet after you shut the system down at the breaker box. Hope this helps and thank you for rating my reply. Tom