Question

Which graph represents the function f (x) = StartFraction 2 Over x minus 1 EndFraction + 4?
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 quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = negative 4.
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 quadrant 3. A vertical asymptote is at x = negative 1, and the horizontal asymptote is at y = negative 4.
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 quadrant 3. A vertical asymptote is at x = negative 1, and the horizontal asymptote is at y = 4.
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 quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 4.

Answer 1

The last graph.

Reason: f(x) = 2/(x−1) + 4 has vertical asymptote x = 1 (denominator zero) and horizontal asymptote y = 4 (as x → ±∞). The numerator 2 > 0 gives the hyperbola branches opening up-right and down-left (relative to the center (1,4)), matching the fourth description.