OG详解-OG7 数学2 Q22

Choice B is correct. An equation that defines a linear function f can be written in the form f(x) = mx+b, where m and b are constants. It’s given in the table that when x =-4, f(x) = 0. Substituting -4 for x and 0 for f(x) in the equation f(x) = mx+b yields 0 = m(-4)+b, or 0 =-4m+b. Adding 4m to both sides of this equation yields 4m = b. Substituting 4m for b in the equation f(x) = mx+b yields  f = mx+4m. It’s also given in the table that when x = −​195​ , f(x)=1. Substituting -19​5​ for x and 1 for f(x) in the equation f(x) = mx+4m yields +4m, or 1 = m(-19​5​) +4m, or 1=
​15​m​ . Multiplying both sides of this equation by 5 yields m = 5. Substituting 5 for m in the equation f(x) = mx+4m yields f(x) = 5x+4(5), or f(x) = 5x+20. If h(x) = f(x)-13, substituting 5x+20 for f(x) in this equation yields h(x) = (5x+20)-13, or h(x) = 5x+7.
Choice A 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. This is an equation that defines the linear function f, not h.