Teresa graphs the following 33 equations: y=2xy=2x, y=x2+2y=x2+2, and y=2x2y=2x2. She says that the graph of y=2xy=2x will eventually surpass both of the other graphs. Is Teresa correct? Why or why not?

the correct question is 
Teresa graphs the following 3 equations: y=2x, y=x2+2, and y=2x2. She says that the graph of y=2x will eventually surpass both of the other graphs. Is Teresa correct? Why or why not?

we have that
y=2x
y=x²+2
y=2x²

using a graph tool
see the attached figure

We can affirm the following
the three graphs present the same domain-----> the interval (-∞,∞)

The range of the graph y=2x  is the interval (-∞,∞)

The range of the graphs y=x²+2 and y=2x² is the interval [0,∞)

therefore
Teresa is not correct because the graph of y = 2x will not surpass the other two graphs since in the interval of [0, infinite) the three graphs present the same range