Question

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

Answer 1

The first graph.

Reason: f(x) = 1/(x+3) − 2 has vertical asymptote where x+3=0 → x = −3 and horizontal asymptote y = −2. The basic 1/x shape with positive coefficient gives branches up-right and down-left relative to the center (−3, −2), which matches the first description.