To complete the table of values for the functions \( f(x) = 8x^2 \) and \( g(x) = 3x + 10 \), we will calculate the values for both functions at \( x = 1, 2, 3, \) and \( 4 \).
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For \( x = 1 \): \[ f(1) = 8(1)^2 = 8 \] \[ g(1) = 3(1) + 10 = 3 + 10 = 13 \]
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For \( x = 2 \): \[ f(2) = 8(2)^2 = 8 \times 4 = 32 \] \[ g(2) = 3(2) + 10 = 6 + 10 = 16 \]
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For \( x = 3 \): \[ f(3) = 8(3)^2 = 8 \times 9 = 72 \] \[ g(3) = 3(3) + 10 = 9 + 10 = 19 \]
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For \( x = 4 \): \[ f(4) = 8(4)^2 = 8 \times 16 = 128 \] \[ g(4) = 3(4) + 10 = 12 + 10 = 22 \]
Now we can summarize the results in a table:
\[ \begin{array}{|c|c|c|} \hline x & f(x) & g(x) \ \hline 1 & 8 & 13 \ 2 & 32 & 16 \ 3 & 72 & 19 \ 4 & 128 & 22 \ \hline \end{array} \]
Both functions \( f(x) \) and \( g(x) \) grow as \( x \) gets larger. However, since \( f(x) = 8x^2 \) is a quadratic function (and thus grows faster than a linear function), it will eventually exceed \( g(x) = 3x + 10 \) for sufficiently large values of \( x \). In our calculations, we can see that even for \( x = 2 \), \( f(x) \) starts to grow much larger than \( g(x) \), and this trend will continue as \( x \) increases. Therefore, \( f(x) \) will eventually exceed \( g(x) \).