OG详解-OG3 数学1 Q12

Choice A is correct. An equation defining a linear function can be written in the form h(x)= ax +b, where a and b are constants. It’s given that h(0)= 41.Substituting 0 for x  and  41 for h(x) in the equation h(x)= ax +b yields 41= a (0)+b, or b = 41. Substituting 41 for b in the equation h(x)= ax +b yields h(x)= ax +41. It’s also given that h(1)= 40. Substituting  1 for x  and  40 for h(x) in the equation h(x)= ax +41 yields 40 = a (1)+41, or 40 = a +41. Subtracting 41 from the left- and right-hand sides of this equation yields  -1= a. Substituting -1 for a  in the equation h(x)= ax +41 yields h(x)=-1x +41, or h (x)=-x +41.
Choice B is incorrect. Substituting 0  for x  and  41 for h(x) in this equation yields 41=-0 , which isn’ta true statement. Choice C is incorrect. Substituting  0 for x  and  41 for h(x) in this equation yields 41=-41(0), or 41= 0, which isn’t a true statement. Choice D is incorrect. Substituting 41 for h(x) in this equation yields 41=-41, which isn’ta true statement.