# Sketch the following functions/relations and supply the domain and range. (Label properly) 9x^2-18x+4y^2-8y=23If it is a function, state whether it is into, onto or one to one and justify.

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### 1 Answer

Let's start by rewriting the equation in standard form.

Factor out the 9 and 4, then complete the square, by adding 1 inside each set of parenthesis. In other words we added 9x1 and 4x1

`9(x^2-2x+1)+4(y^2-2y+1)=23+4+9`

`9(x-1)^2+4(y-1)^2=36` Divide both sides by 36 we get

`(x-1)^2/4+(y-1)^2/9=1`

Since the number under the y is larger that means we have an ellipse with a vertical major axis.

The center of the ellipse is at (1,1).

The vertices on the major axis are (1,1+3) and (1,1-3) => (1,4) and (1,-2).

The vertices on the minor axis are (1+2,1) and (1-2,1) => (3,1) and (-1,1)

Sorry the program we are using can't be used to graph ellipse. Hope the above info was helpful.

B) Domain [-1,3] and range [-2,4]

C) It is not a function, since if fails the vertical line test.