1. **State the problem:** We need to complete the table of values for the functions $f(x) = 5x + 4$ and $g(x) = x^2 + 2x + 3$ at $x = 2, 3, 4, 5$. 2. **Calculate $f(x)$ values:** - For $x=2$: $$f(2) = 5(2) + 4 = 10 + 4 = 14$$ - For $x=3$: $$f(3) = 5(3) + 4 = 15 + 4 = 19$$ - For $x=4$: $$f(4) = 5(4) + 4 = 20 + 4 = 24$$ - For $x=5$: $$f(5) = 5(5) + 4 = 25 + 4 = 29$$ 3. **Calculate $g(x)$ values:** - For $x=2$: $$g(2) = 2^2 + 2(2) + 3 = 4 + 4 + 3 = 11$$ - For $x=3$: $$g(3) = 3^2 + 2(3) + 3 = 9 + 6 + 3 = 18$$ - For $x=4$: $$g(4) = 4^2 + 2(4) + 3 = 16 + 8 + 3 = 27$$ - For $x=5$: $$g(5) = 5^2 + 2(5) + 3 = 25 + 10 + 3 = 38$$ 4. **Complete the table:** | x | f(x) | g(x) | |---|------|------| | 2 | 14 | 11 | | 3 | 19 | 18 | | 4 | 24 | 27 | | 5 | 29 | 38 | 5. **Compare growth of $f(x)$ and $g(x)$:** - $f(x)$ is a linear function with slope 5. - $g(x)$ is a quadratic function, which grows faster than any linear function as $x$ becomes very large. 6. **Conclusion:** - For small $x$, $f(x)$ may be larger. - As $x$ increases, $g(x)$ eventually exceeds $f(x)$ because quadratic growth outpaces linear growth. Therefore, $g(x)$ eventually exceeds $f(x)$ as $x$ gets larger.