Question

tell whether each graph is a function and justify your answer. which graph is not a good representation of a real - world situation? explain. graph a (with x - axis time from 0 - 9, y - axis distance from 0 - 9, a curved line), graph b (with x - axis time from 0 - 9, y - axis distance from 0 - 9, a curved line). dropdowns: blank is a function because blank corresponds blank one blank

Explanation:

Step1: Recall the Vertical Line Test

A graph represents a function if every vertical line intersects the graph at most once. This is because in a function, each input (x - value) should have exactly one output (y - value).

Step2: Analyze Graph A

For Graph A, if we draw a vertical line (for example, at a certain x - value in the region where the graph has a "zig - zag"), the vertical line will intersect the graph more than once. So, Graph A does not pass the vertical line test, meaning it is not a function.

Step3: Analyze Graph B

For Graph B, any vertical line drawn will intersect the graph at most once. So, Graph B passes the vertical line test, meaning it is a function.

Step4: Real - World Situation Analysis

In a real - world situation where we have time (x - axis) and distance (y - axis), distance is a function of time. That is, at any given time (input), there should be exactly one distance (output) from a starting point. Since Graph A is not a function, it cannot represent a situation where distance depends on time (because at a single time, there would be multiple distances, which doesn't make sense in a real - world context of motion where at a specific time, an object is at one distance from the start). Graph B, being a function, can represent a real - world situation where an object moves (e.g., speeds up, slows down, changes direction but at each time has one distance from the start). So, Graph A is not a good representation of a real - world situation (relating time and distance) because it violates the definition of a function (one input, one output) which is required for such a real - world relationship.

Answer:

Graph B is a function because each x - value (time) corresponds to exactly one y - value (distance). Graph A is not a function. Graph A is not a good representation of a real - world situation (relating time and distance) because in a real - world context of motion, at a given time, an object should be at only one distance from a starting point, but Graph A (not a function) would imply multiple distances at the same time, which is not physically meaningful.