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April 22nd, 2017, 11:43 PM   #1
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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.
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April 23rd, 2017, 12:22 AM   #2
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No. As y = 0 for x = 0, 0 is in the range.
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