OG详解-OG2 数学1 Q24

Choice A is correct. An equation for the graph shown can be written in slope-intercept form y = mx + b, where m  is the slope of the graph and itsy-intercept  is (0, b). Since they-intercept of the graph shown is  (0, 2), the value of b is  2.  Since the graph also passes through the point  (4, 1), the slope can be calculated  as  1−24−0​​ , or - 1​4​. Therefore, the value of m  is -1​4​. Substituting  -1​4 for m and 2 for b in the equation y = mx + b yields y = -1​4x + 2 . It’s given that an equation for the graph shown is y = f (x)+14. Substituting f(x)+14 for y  in the equation y = - 1​4x +2  yields  f(x)+14 = -1​4x+2. Subtracting 14  from both sides of this equation yields f(x )= - 1​4x -12 .
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.