Malachi Durham

Mathematics

10 September, 14:09

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=2x2 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=2x2 because the yy-value is always twice the value of x2x2.

C. Teresa is not correct.

The graph of y=2x2y=2x2 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.