My Math Forum Is "The range of g(x) is all real numbers" wrong?

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 April 22nd, 2017, 11:43 PM #1 Senior Member   Joined: Apr 2008 Posts: 193 Thanks: 3 Is "The range of g(x) is all real numbers" wrong? Consider the function g(x) = 2x/(4x^2 + 7x -2). Which statement is false below? (a) g(x) has two vertical asymptotes. (b) g(x) has the domain in which "x is not equal to -1/4 and 2". (c) g(x) has a horizontal asymptote along y = 0. (d) g(x) has the range in which y is all real numbers. My answer is (b) is false because x = 1/4 and x = -2. The answer key says (b). So, my answer is correct, but shouldn't (d) is false as well? The reason is that g(x) has a horizontal asymptote along y = 0. Did the answer key overlook (d)? Thanks for your help.
 April 23rd, 2017, 12:22 AM #2 Global Moderator   Joined: Dec 2006 Posts: 19,057 Thanks: 1618 No. As y = 0 for x = 0, 0 is in the range.

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