OG详解-OG2 数学1 Q15

Choice D is correct. Since f is a linear function, it can be defined by an equation of the form f(x)= ax +b, where a and b are constants. It’s given that f(0)=8. Substituting 0 for x and 8 for f(x) in the equation f(x)= ax +b yields 8= a(0)+b, or 8= b. Substituting 8 for b in the equation f(x)= ax +b yields f(x)= ax +8. It’s given that f(1)=12. Substituting 1 for x and 12 for (f x) in the equation f(x)= ax +8 yields 12= a(1)+8, or 12= a+8. Subtracting 8 from both sides of this equation yields a = 4. Substituting 4 for a in the equation f(x)= ax +8 yields f(x)= 4x +8. Therefore, an equation that defines f is f(x)= 4x +8.
Choice A is incorrect and may result from conceptual or calculation errors. 
Choice B is incorrect and may result from conceptual or calculation errors. 
Choice C is incorrect and may result from conceptual or calculation errors.