Question

1. the graph shows the distance, y, a student swims from one boat dock to another in a lake after x minutes of swimming. which scenario best represents the graph? a the student starts swimming at a fast rate, stops and treads water, then swims at a slower rate. b the student starts swimming at a fast rate, transitions to a slower rate, then stops swimming. c the student starts swimming at a slow rate, accelerates to a faster rate, then swims at a slower rate. d the student swims at the same, fast rate for the entire swim. 36. consider the table. which statement is true? a the table is a function because for each input value, there is exactly one output value. b the table is a function because for the input value of 2, there is more than one output value. c the table is not a function because for each input value, there is exactly one output value. d the table is not a function because for the input value of 2, there is more than one output value.

Explanation:

Question 35

Step1: Analyze the graph's segments

The graph has three segments: a steep line (fast rate), a horizontal line (distance constant, so treading water/stopped), and a less steep line (slower rate).

Step2: Match with options

• Option A: Fast rate, stop/tread, slower rate. Matches the graph segments.
• Option B: Ends with stopping, but graph has a third segment (not stopping). Incorrect.
• Option C: Starts slow, but first segment is steep (fast). Incorrect.
• Option D: Constant rate, but graph has flat and less steep segments. Incorrect.

Step1: Recall function definition

A function is a relation where each input (x - value) has exactly one output (y - value).

Step2: Analyze the table

For x = 2, y has values 9 and - 6. So one input (2) has multiple outputs. Thus, it is not a function.

Step3: Match with options

• Option A: Incorrect, since x = 2 has two y - values.
• Option B: Incorrect, a function can't have one input with multiple outputs.
• Option C: Incorrect, the reason given is for a function, but the table is not a function.
• Option D: Correct, as x = 2 has more than one y - value, so it's not a function.

Answer:

A. The student starts swimming at a fast rate, stops and treads water, then swims at a slower rate.

Question 36