1. **State the problem:** We need to determine which of the given input-output pairs satisfy the function $y = x^3$. 2. **Recall the function:** The function is defined as $y = x^3$, meaning for each input $x$, the output $y$ is the cube of $x$. 3. **Check each pair:** - A. $(-1, -1)$: Calculate $(-1)^3 = -1$. Matches output $-1$. Valid. - B. $(-2, 8)$: Calculate $(-2)^3 = -8$. Output is $8$, does not match. Invalid. - C. $(3, 9)$: Calculate $3^3 = 27$. Output is $9$, does not match. Invalid. - D. $(\frac{1}{2}, \frac{1}{8})$: Calculate $\left(\frac{1}{2}\right)^3 = \frac{1}{8}$. Matches output $\frac{1}{8}$. Valid. - E. $(4, 64)$: Calculate $4^3 = 64$. Matches output $64$. Valid. - F. $(1, -1)$: Calculate $1^3 = 1$. Output is $-1$, does not match. Invalid. 4. **Final answer:** The valid input-output pairs for $y = x^3$ are A, D, and E.