Question

which graph displays a function with a range of $y \leq -4$?

Explanation:

The range \(y \leq -4\) means all output values of the function are less than or equal to -4, so the graph must open downward with its maximum vertex at \(y = -4\), and all points lie below or on this line.

• Option A: Opens upward, range is \(y \geq -4\) (incorrect).
• Option B: Opens downward, vertex at \(y = -4\), all points are \(y \leq -4\) (correct).
• Option C: Opens downward, vertex is above \(y = -4\), so range includes values greater than -4 (incorrect).
• Option D: Opens upward, range is \(y \geq -4\) (incorrect).

Answer:

B. The downward-opening parabola with vertex at \(y=-4\) (the top-right graph)