Question

Which graph represents the function f (x) = StartFraction 4 Over x EndFraction?
On a coordinate plane, a hyperbola is shown. A curve opens up and to the right in quadrant 1, and another curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 0.
On a coordinate plane, a hyperbola is shown. A curve opens up and to the right in quadrant 1, and another curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 0.25.
On a coordinate plane, a hyperbola is shown. A curve opens up and to the left in quadrant 2, and another curve opens down and to the right in quadrant 4. A vertical asymptote is at x = 0.
On a coordinate plane, a hyperbola is shown. A curve opens up and to the left in quadrant 2, and another curve opens down and to the right in quadrant 4. A vertical asymptote is at x = 0.25.

Answer 1

The first graph. For f(x)=4/x, y>0 when x>0 and y<0 when x<0, so the branches are in quadrants I and III, and the vertical asymptote is x=0 (also horizontal asymptote y=0).