x f ( x ) 0 29 1 32 2 35 For the linear function f

Choice A is correct. An equation that defines a linear function $f$ can be written in the form $f\left(x\right)=mx+b$, where $m$ and $b$ are constants. It's given in the table that when $x=0$, $f\left(x\right)=29$. Substituting $0$ for $x$ and $29$ for $f\left(x\right)$ in the equation $f\left(x\right)=mx+b$ yields $29=m\left(0\right)+b$, or $29=b$. Substituting $29$ for $b$ in the equation $f\left(x\right)=mx+b$ yields $f\left(x\right)=mx+29$. It's also given in the table that when $x=1$, $f\left(x\right)=32$. Substituting $1$ for $x$ and $32$ for $f\left(x\right)$ in the equation $f\left(x\right)=mx+29$ yields $32=m\left(1\right)+29$, or $32=m+29$. Subtracting $29$ from both sides of this equation yields $3=m$. Substituting $3$ for $m$ in the equation $f\left(x\right)=mx+29$ yields $f\left(x\right)=3x+29$.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.