f x = x + 6 x - 4 If the given function f is graphed in the xy -plane,

Question

f x = x + 6 x - 4 If the given function f is graphed in the xy -plane, where y = f x , what is the x -coordinate of an x -intercept of the graph?

Accepted Answer

The correct answer is either - 6 or 4 . The x -intercepts of a graph in the xy -plane are the points where y = 0 . Thus, for an x -intercept of the graph of y = f x , 0 = f x . Substituting 0 for f x in the equation f x = x + 6 x - 4 yields 0 = x + 6 x - 4 . By the zero product property, x + 6 = 0 and x - 4 = 0 . Subtracting 6 from both sides of the equation x + 6 = 0 yields x = - 6 . Adding 4 to both sides of the equation x - 4 = 0 yields x = 4 . Therefore, the x -coordinates of the x -intercepts of the graph of y = f x are - 6 and 4 . Note that -6 and 4 are examples of ways to enter a correct answer.

Question e3e1bd