SOLUTION: a, sketch the graph of the relation {(x,y):(y-4)^2=x+2}. b, state the implied domain and range of this station. c, explain with reasons whether this relation is a function.

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Question 875670: a, sketch the graph of the relation
{(x,y):(y-4)^2=x+2}.
b, state the implied domain and range of this station.
c, explain with reasons whether this relation is a function.
Found 2 solutions by ewatrrr, josgarithmetic:
Answer by ewatrrr(24785) (Show Source):
You can put this solution on YOUR website!

Re:TY
Need to Know.......................................................
Standard Form of an Equation of a Circle is
Standard Form of an Equation of an Ellipse is
Standard Form of an Equation of an Hyperbola opening up and down is:
Standard Form of an Equation of an Hyperbola opening right and left is:
the vertex form of a Parabola opening up(a>0) or down(a<0),
the vertex form of a Parabola opening right(a>0) or left(a<0),
where(h,k) is the vertex and y = k is the Line of Symmetry
x = (y-4)^2 -2 Parabola Opening right along y = 4, V(-2,4)
y = 4 � sqrt(x+2), Domain x > -2
c: not a function, will not satisfy the vertical line test. Note x = 5 (Blue vertical line)
(2 values of y for one x-value )

Answer by josgarithmetic(39618) (Show Source):
You can put this solution on YOUR website!
Parabola in standard form, and graph has horizontal symmetry axis. Vertex (-2,4). Parabola opens to the right. This is a relation, not a function. The graph is two functions put together. You see in the graph each point of the graph shares the same x value as one other point,except the vertex. Each y value has two x values, so the graph is not a function. No points occur to the left of .

Domain is Real numbers greater than -2.
Range is all Real numbers.