Evaluating Expressions for Different Values of x

5.9.1 Evaluating Expressions for Different Values of x

5.9.1 • Evaluating Expressions for Different Values of x

Warm Up

Lin and Diego are discussing two expressions: $x^{2}$ and $2^{x}$ .

Lin says, “I think the two expressions are equivalent.”
Diego says, “I think the two expressions are only equal for some values of $x$ .”

Do you agree with either of them? Explain or show your reasoning.

Your answer may vary, but here is a sample:

I agree with Diego. Sample explanation: If we find the value of $x^{2}$ and $2^{x}$ for different values of $x$ , say 0, 1, 2, 3, and 4, we can see that they are not always equal. As the table shows, they are only equal sometimes, for example, when $x$ is 2 and 4.

$x$	$x^{2}$	$2^{x}$
1	1	2
2	4	4
3	9	8
4	16	16
5	25	32
10	100	1,024