Question

warm-up
select all the graphs showing relations that are also functions.

Explanation:

To determine which graphs represent functions, we use the vertical line test: a graph is a function if no vertical line intersects it more than once.

Analyzing each graph:

• Graph A: A vertical line (e.g., \( x = 0 \)) intersects the graph twice. Not a function.
• Graph B: Each \( x \)-value (horizontal coordinate) has only one \( y \)-value (vertical coordinate). Passes the vertical line test. Function.
• Graph C: Each \( x \)-value has only one \( y \)-value. Passes the vertical line test. Function.
• Graph D: A parabola - shaped graph. No vertical line intersects it more than once. Passes the vertical line test. Function.
• Graph E: A straight line (linear graph). No vertical line intersects it more than once. Passes the vertical line test. Function.
• Graph F: A vertical line (e.g., \( x = -1 \)) — a vertical line itself intersects infinitely many times. Fails the vertical line test. Not a function.

Answer:

Graph B, Graph C, Graph D, Graph E