Rational Functions — Test

Question 3 • Precalculus

Which graph represents the function f of x is equal to 4 over x ?

Answer

Image with description A coordinate plane with a graph showing two branches. The branch on the left approaches the x-axis as x approaches negative infinity from the right and approaches the y-axis as x approaches 0 from the left. Its turning point is near (negative 2 comma 2). The branch on the right approaches the y-axis as x approaches 0 from the right and approaches the x-axis as x approaches infinity from the left. Its turning point is near (2 comma negative 2).

Image with description A line graph on a Cartesian coordinate plane shows a rational function with two separate branches. The x-axis and y-axis are labeled with even integer values from negative 8 to 8. One branch lies in the first quadrant, passing through (1 comma 1) and approaching both axes without touching them. The second branch lies in the third quadrant, passing through (negative 1 comma negative 1) and also approaching both axes asymptotically.

Image with description A coordinate plane with a graph showing two branches. The branch on the left approaches the x-axis as x approaches negative infinity from the right and approaches the y-axis as x approaches 0 from the left. Its turning point is near (negative 2 comma negative 2). The branch on the right approaches the y-axis as x approaches 0 from the right and approaches the x-axis as x approaches infinity from the left. Its turning point is near (2 comma 2).

Image with description A coordinate plane with a graph showing two branches. The branch on the left approaches the x-axis as x approaches negative infinity from the right and approaches the y-axis as x approaches 0 from the left. Its turning point is near (negative 1 comma 1). The branch on the right approaches the y-axis as x approaches 0 from the right and approaches the x-axis as x approaches infinity from the left. Its turning point is near (1 comma negative 1).

Explanation

For f(x) = 4/x, positive x-values give positive y-values, and negative x-values give negative y-values, so the branches lie in quadrants I and III. Substituting x = 2 gives y = 2, and x = -2 gives y = -2, matching the graph described in choice A. The x- and y-axes are asymptotes.

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