Context: A linear function $h$ has a graph that lies completely inside quadrants I and II of the $xy$-plane, never entering III or IV. We need a rule that could define $h$.

Answer: D) $h(x) = 46$

Why? Quadrants I and II are the two regions above the $x$-axis, so the line must stay above that axis for every $x$. A line with any nonzero slope eventually crosses the $x$-axis and drops into a lower quadrant, so the graph must be horizontal and positioned above the axis. That is exactly $y = 46$, a horizontal line $46$ units up.

Traps:

• A) $h(x) = 46x + 46$ has a positive slope, so for $x < -1$ it falls below the $x$-axis and enters quadrant III.
• B) $h(x) = -46$ is horizontal but sits below the $x$-axis, lying entirely in quadrants III and IV.
• C) $h(x) = 46x$ passes through the origin with positive slope, running through quadrants III and I.