sat-dog

Choice A is correct. It’s given that the table shows values of x and their corresponding values of g^xh, where g^xh =f + ^xh. It’s also given that f is a linear x 3 function. It follows that an equation that defines f can be written in the form = + f^xh mx b, where m represents the slope and b represents the y-coordinate 0, = of the y-intercept ^ bh of the graph of y f^xh in the xy-plane. The slope of the graph of y = f^xh can be found using two points, ^x1 , y1 h and ^x2 , y2 h, that are on the = =y2- y1 graph of y f^xh, and the formula m x2- x1. Since the table shows values of x and their corresponding values of g^xh, substituting values of x and g^xh in the equation g^xh =f + ^xh can be used to define function f. Using the first pair of values from the table, x x =- 3 27 and g^xh = 3, yields 3= - f^2 - 7 2 + 7 h3, or 3=f^ - - 2 2 4 7 h. Multiplying -24 -72= -27 -27,-72 each side of this equation by yields f^ h, so the point ^ h 42 SAT PRACTICE TEST #6 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 1 = =- is on the graph of y f^xh. Using the second pair of values from the table, x 9 and g^xh = 0, yields 0= - f^9 - + 9 h3, or 0=f^ - - 6 9 h. Multiplying each side of this equation - 0= -9 -9,0 = by 6 yields f^ h, so the point ^ h is on the graph of y f^xh. Substituting ^ -27,-72 h and ^ -9,0 h for ^x1 , y1 h and ^x2 , y2 h, respectively, in the formula m =y x = 2 2 - - y x1 1 y + ields m = - 0 9 - - ^ = - ^ - 7 2 2 7h h + , or m = 4. 0 S = ubst - itu 9 ting 4 for m in - the equation f^xh mx b yields f^xh 4x b. Since f^ h, substituting 9 for = + 0=4 -9+ x and 0 for f^xh in the equation f^xh 4x b yields ^ h b, or 0=-36+ 36 36= b. Adding to both sides of this equation yields b. It follows that 36 0, = is the y-coordinate of the y-intercept ^ bh of the graph of y f^xh. Therefore, = 0,36 the y-intercept of the graph of y f^xh is ^ h. 12 Choice B is incorrect. is the y-coordinate of the y-intercept of the graph of = = y g^xh. Choice C is incorrect. 4 is the slope of the graph of y f^xh. Choice D is - = incorrect. 9 is the x-coordinate of the x-intercept of the graph of y f^xh.