1. **Problem Statement:** We have two function machines. The first squares the input number (raises it to the power 2). The second cubes the input number (raises it to the power 3). 2. **Formulas:** - For the first machine: $$y = x^2$$ - For the second machine: $$y = x^3$$ 3. **Completing the outputs for the first machine (squaring):** - Input 2: Output is $$2^2 = 4$$ (given) - Input 4: Output is $$4^2 = 16$$ - Input 5: Output is $$5^2 = 25$$ 4. **Completing the outputs for the second machine (cubing):** - Input 2: Output is $$2^3 = 8$$ (given) - Input 4: Output is $$4^3 = 64$$ - Input 5: Output is $$5^3 = 125$$ 5. **Table of values for the first machine:** | x | 2 | 4 | 5 | |---|---|----|----| | y | 4 | 16 | 25 | 6. **Table of values for the second machine:** | x | 2 | 4 | 5 | |---|---|----|-----| | y | 8 | 64 | 125 | **Explanation:** - Squaring a number means multiplying it by itself. - Cubing a number means multiplying it by itself twice more (three times total). - So, for any input $$x$$, the output is $$x^2$$ for the first machine and $$x^3$$ for the second. Final answers: - First machine outputs: 4, 16, 25 - Second machine outputs: 8, 64, 125