1. The problem gives a table of values for a linear function $f(x)$: $$\begin{array}{c|c} x & f(x) \\ \hline 0 & 29 \\ 1 & 32 \\ 2 & 35 \end{array}$$ We need to find the equation of the form $f(x) = mx + b$ that fits these points. 2. Recall the formula for a linear function: $$f(x) = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. The y-intercept $b$ is the value of $f(x)$ when $x=0$. From the table, when $x=0$, $f(x)=29$, so: $$b = 29$$ 4. Next, find the slope $m$ using two points, for example $(0,29)$ and $(1,32)$: $$m = \frac{f(1) - f(0)}{1 - 0} = \frac{32 - 29}{1} = 3$$ 5. So the equation is: $$f(x) = 3x + 29$$ 6. Check with the third point $(2,35)$: $$f(2) = 3(2) + 29 = 6 + 29 = 35$$ which matches the table. 7. Therefore, the correct equation is option A) $f(x) = 3x + 29$.