4x^2+4y^2=64
what are the domain and range

Use a graphing tool and you'll see a circle form. This circle has a center of (0,0) and radius of 4. Side note: this equation is equivalent to x^2+y^2 = 16 after you divide everything by 4

Looking at the graph, the smallest x can be is -4. The largest x can be is 4. So the domain in interval notation is 

Similarly the range in interval notation is also  because the lowest you can go is y = -4. The highest you can go is y = 4