Let $$F : R^2 \rightarrow R^4$$ be $$F (x; y) = (x^3y, sin(xy), 3, xy^3)$$. Answer with explanations:

i) Which [IEQ]R^k[/IEQ] is the graph of F a subset of ?;

I would say R^4 due to 4 varibles being required to describe the output.

ii) Write the equation of the graph of F ?;

a=x^3y; b=sin(xy), c=3, d=xy^3

iii) What is the dimension of the graph of F ?

2, due to only two value being needed to describe the shape of the graph (x and y)

Can someone tell me if these are right?

Question

Let $$F : R^2 \rightarrow R^4$$ be $$F (x; y) = (x^3y, sin(xy), 3, xy^3)$$. Answer with explanations:

i) Which [IEQ]R^k[/IEQ] is the graph of F a subset of ?;

I would say R^4 due to 4 varibles being required to describe the output.

ii) Write the equation of the graph of F ?;

a=x^3y; b=sin(xy), c=3, d=xy^3

iii) What is the dimension of the graph of F ?

2, due to only two value being needed to describe the shape of the graph (x and y)

Can someone tell me if these are right?