Question

if represents a function, only one of the graph choices presented will have a single solution to the equation ( f(x) = -3 ). which one is it? choose the correct graph below.

Explanation:

To find which graph has a single solution to $f(x) = -3$, we check how many times the horizontal line $y=-3$ intersects each graph:

1. Graph A: The horizontal line $y=-3$ intersects the graph at infinitely many points (it aligns with a horizontal segment of the graph), so it has infinitely many solutions.
2. Graph B: The horizontal line $y=-3$ intersects the graph at exactly one point, so it has a single solution.
3. Graph C: The horizontal line $y=-3$ intersects the graph at two distinct points, so it has two solutions.
4. Graph D: The horizontal line $y=-3$ intersects the graph at infinitely many points (aligns with a horizontal segment), so it has infinitely many solutions.

Answer:

B. The graph that intersects the line $y=-3$ exactly once