Question

Teresa graphs the following 3 equations: y=2x, y=x2+2, and y=2×2.

She says that the graph of y=2x will eventually surpass both of the other graphs.

Is Teresa correct? Why or why not?\

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.