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The easiest way to do this is to have a voice coach help you, but you can figure it out on your own. Start with a middle C on a keyboard. Play it and match it with your voice. Do this again with the next note down and continue until you reach a note you cannot sing without straining your vocal cords. This is the bottom of your range. Repeat this process going up in pitch to find the top of your range. Search online for videos of notes played up and down the keyboard if you don't have access to a keyboard. Start with your normal range. Repeat a simple sound such as "la," moving up and down your range. Master that first, touching upon notes at the high and low end of the range. Don't linger on notes that put a strain on your throat. Focus on staying relaxed and breathing properly. Perform scales at least eight to ten times a day in practice. Continue this range practice daily until you can hit the difficult notes eight to ten times in a session. Continue to use the scale exercise, attempting to sustain difficult notes for longer periods of time. Add in other exercises to loosen your vocal cords. Take a break whenever you feel uncomfortable. The more you reach these notes, the easier time you'll have singing them without pain. One exercise you can add is slides. Sing a note. Instead of moving back and forth, stop at the next note. Do this for each note until you reach the end of your range. Another exercise is to grunt. Grunt to shorten your vocal cords, then sing a short word like "mom" in a note in your range. Move up or down your range each time.
Find your natural range. Move through your normal range. Work up to difficult notes.