OG详解-OG3 数学1 Q24

Choice C is correct. It’s given that  f(x)=ax+b​​ and that the graph shown is a partial graph of y = f (x). Substituting y  for f(x) in the equation f(x)=ax+b yields y = ax+b​​. The graph passes through the point (-7, -2). Substituting -7 for x  and -2  for y  in the equation  y = ax+b yields -2 = a-7+b  . Multiplying each side of this equation by -7 +b yields -2(-7 +b)= a , or 14 -2b = a. The graph also  passes through the point (-5, -6). Substituting -5 for x and -6  for y in the equation  y = ax+b yields -6 = a−5​+b​  . Multiplying each side of this equation by -5 + b yields -6(-5 + b)= a , or 30 -6b = a. Substituting 14 -2b for a  in this  equation yields 30-6b = 14 -2b. Adding 6b to each side of this equation yields 30 = 14 + 4b. Subtracting 14  from each side of this equation yields 16 = 4b. Dividing each side of this equation by 4 yields  4 = b. Substituting 4 for b in the equation 14 -2b = a yields 14 -2(4)= a, or 6 = a. Substituting 6 for a and 4 for b in the equation  f(x)=ax+b​​ yields  f(x)=a6+4. It’s given thatg(x)=f(x+4​). Substituting x + 4 for x  in the equation f yields f  which is equivalent to f(x+4)=6x+8​​. It follows that g(x​)=6x+8​          .
Choice A is incorrect. This could define function g  if  g(x)= f (x -4). Choice B is incorrect. This could define function g  if  g(x)= f (x). Choice D is incorrect. This could define function g if g(x)= f (x) · (x + 4).