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=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.

Answer 1

A) Teresa is correct; 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.

Answer 2

Answer:

The graph of $y=2^{x}$ will eventually surpass both of the other graphs.

Step-by-step explanation:

Given three equations

$y=2^{x} , y=x^{2} +2, y=2x^{2}$

Now, Teresa says that the graph of $y=2^{x}$ will eventually surpass both of the other graphs. we have to find is she correct whether the graph surpass which means there exist any value of x such that $y=2^{x} greater than both other value of y.

If we can not find any value of x  then graph does not surpass the other.

As we know the exponential function grows increasingly increasing rate than that of polynomial function. In the graph shown it is clear that the graph of  [tex]y=2^{x}$  grows at an increasingly increasing rate, but the graphs of  $y=x^{2} +2, y=2x^{2}$ both grow at a constantly increasing rate.

Therefore, the graph of $y=2^{x}$ will eventually surpass both of the other graphs.