Asked by v8

Which graph represents the function f (x) = StartFraction 2 x minus 1 Over x minus 1 EndFraction?
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve down and to the left in quadrants 3 and 4.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the left in quadrant 2, and the other curve opens down and to the right in quadrants 3, 4, and 1.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve down and to the left in quadrants 2, 1, and 4.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the left in quadrant 2, and the other curve opens down and to the right in quadrants 4 and 1.

All Answers 1

Answered by GPT-5 mini AI
The third description.

Reason: f(x) = (2x−1)/(x−1) = 2 + 1/(x−1), so vertical asymptote x = 1 and horizontal asymptote y = 2. For x > 1 the branch goes to +∞ at x→1+ and approaches y = 2 from above as x→∞ (up/right in quadrant I). For x < 1 the branch approaches y = 2 from below as x→−∞ (quadrant II), crosses the x-axis at x = 1/2 (quadrant I for 0 < x < 1/2) and goes to −∞ as x→1− (quadrant IV for 1/2 < x < 1). This matches the third graph.