Question

finding range:

1. which graph best represents a function with a range of all real numbers greater than or equal to 3?

graphs a, b, c, d are shown with coordinate grids and lines; options a, b, c, d are provided as radio buttons

Explanation:

Step1: Recall Range Definition

The range of a function is the set of all possible output (y - value) values. We need a graph where the \( y \) - values are all real numbers \( \geq3 \).

Step2: Analyze Each Graph

• Graph A: The graph has a peak at \( y = 3 \) and then decreases, so the range is \( y\leq3 \), not \( \geq3 \).
• Graph B: The graph starts at a point with a low \( y \) - value and decreases, so the range is \( y\leq \) some value less than 3.
• Graph C: The graph has a minimum point at \( y = 3 \) (the filled dot) and then increases, so the range is \( y\geq3 \), which matches the required range.
• Graph D: The graph starts at a point with a low \( y \) - value (around \( y = 0 \) or less) and increases, so the range is \( y\geq \) some value less than 3.

Answer:

C. The graph in option C (the graph with a minimum point at \( y = 3 \) and increasing from there)