Need . does the graph represent function explain

Yes it is a function. Why? This is because every input (x value) has only one output (y value). We can also test this by using the vertical line test. To do this draw vertical lines through the graph. If a lines passes through the graph more than once it is not a function.

g(x) = x² + 2

step-by-step explanation:

it is given that the graphs are the same shape.

the only difference is that the red graph is 2 units higher than the blue graph.

that is to say that the red graph is simply the blue graph that has been moved vertically by 2 units in the positive y direction.

hence

g(x) = f(x) + 2

or

g(x) = x² + 2