1. **State the problem:** We are given three functions: $f(x) = x^2$, $g(x) = 2x$, and $h(x) = x^2 - 2x$. We need to fill in the table of values for $f(x)$ and $g(x)$ at $x = -2, -1, 0, 1, 2$ and compare their outputs. 2. **Recall the formulas:** - $f(x) = x^2$ means we square the input value. - $g(x) = 2x$ means we multiply the input value by 2. 3. **Calculate $f(x)$ values:** - For $x = -2$: $f(-2) = (-2)^2 = 4$ - For $x = -1$: $f(-1) = (-1)^2 = 1$ - For $x = 0$: $f(0) = 0^2 = 0$ - For $x = 1$: $f(1) = 1^2 = 1$ - For $x = 2$: $f(2) = 2^2 = 4$ 4. **Calculate $g(x)$ values:** - For $x = -2$: $g(-2) = 2 \times (-2) = -4$ - For $x = -1$: $g(-1) = 2 \times (-1) = -2$ - For $x = 0$: $g(0) = 2 \times 0 = 0$ - For $x = 1$: $g(1) = 2 \times 1 = 2$ - For $x = 2$: $g(2) = 2 \times 2 = 4$ 5. **Fill the table:** | x | f(x) = x^2 | g(x) = 2x | |-----|------------|-----------| | -2 | 4 | -4 | | -1 | 1 | -2 | | 0 | 0 | 0 | | 1 | 1 | 2 | | 2 | 4 | 4 | 6. **Compare outputs:** - $f(x)$ outputs are always non-negative because squaring any real number is non-negative. - $g(x)$ outputs are linear and can be negative or positive depending on $x$. - At $x=0$ and $x=2$, both functions have the same output value 0 and 4 respectively. This completes the comparison of $f(x)$ and $g(x)$ for the given inputs.