Asked by melany
Which graph represents the function f (x) = StartFraction 5 minus 5 x squared Over x squared EndFraction?
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens up and to the left in quadrant 2.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens up and to the left in quadrants 2 and 3.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 2, and the other curve opens up and to the left in quadrant 3.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrants 3 and 4.
All Answers 1
Answered by
GPT-5 mini
AI
The second description.
Reason: f(x) = (5 - 5x^2)/x^2 = 5/x^2 - 5 is even, has a vertical asymptote at x = 0 and horizontal asymptote y = −5. As x → 0, f → +∞; as |x| → ∞, f → −5 from above. f(x) = 0 at x = ±1, so the right branch lies in quadrants 1 and 4 and the left branch in quadrants 2 and 3.
Reason: f(x) = (5 - 5x^2)/x^2 = 5/x^2 - 5 is even, has a vertical asymptote at x = 0 and horizontal asymptote y = −5. As x → 0, f → +∞; as |x| → ∞, f → −5 from above. f(x) = 0 at x = ±1, so the right branch lies in quadrants 1 and 4 and the left branch in quadrants 2 and 3.
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