Answers

1. Based on the information, A.Teresa is correct. The graph of y=2xy=2x grows at an increasingly increasing rate, but the graphs of y=x2+2y=x2+2 and y=2x2y=2×2 both grow at a constantly increasing rate. Therefore, the graph of y=2xy=2x will eventually surpass both of the other graphs.

   How to explain the graph?

   It should be noted that a graph is simply used to show the relationship that exists in the data given diagrammatically.

   It should be noted that Teresa is correct as y=2ˣ grows at an increasingly increasing rate, while the other two grow at a constantly increasing rate. This means y=2ˣ will surpass the other two.

   In conclusion, the correct option is A.

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   Complete question

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

   A.Teresa is correct.

   The graph of y=2xy=2x grows at an increasingly increasing rate, but the graphs of y=x2+2y=x2+2 and y=2x2y=2×2 both grow at a constantly increasing rate.

   Therefore, the graph of y=2xy=2x will eventually surpass both of the other graphs.

   B. Teresa is not correct.

   The graph of y=2xy=2x grows at an increasing rate and will eventually surpass the graph of y=x2+2y=x2+2.

   However, it will never surpass the graph of y=2x2y=2×2 because the yy-value is always twice the value of x2x2.

   C. Teresa is not correct.

   The graph of y=2x2y=2×2 already intersected and surpassed the graph of y=2xy=2x at x=1x=1.

   Once a graph has surpassed another graph, the other graph will never be higher.

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