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is the graph a function or not a function

input output
2 20
4 40
3 30
2 40

3 answers

To determine if the given relation is a function, we need to check if each input is associated with exactly one output.

In your provided data:

  • Input 2 has outputs 20 and 40 (not a function since input 2 maps to two different outputs).
  • Input 4 has output 40.
  • Input 3 has output 30.

Since the input 2 has more than one output, this relation is not a function. A function must have a unique output for each input.

Which scenario best describes the graph:
the graph starts at (0,30) and ends at (10, 0)

(1 point)
Responses

Juan starts with $30 in savings and increases his savings amount by $1 each week.
Juan starts with $30 in savings and increases his savings amount by $1 each week.

Juan saves $30 per week.
Juan saves $30 per week.

Juan starts with $30 in savings and increases his savings amount by $5 each week.
Juan starts with $30 in savings and increases his savings amount by $5 each week.

Juan starts with $5 in savings and increases his savings amount by $30 each week.
Juan starts with $5 in savings and increases his savings amount by $30 each week.
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To analyze the graph that starts at (0, 30) and ends at (10, 0), we need to consider what these points mean in the context of savings over time:

  • The starting point (0, 30) indicates that at week 0, Juan has $30 in savings.
  • The endpoint (10, 0) indicates that at week 10, Juan has $0 in savings.

This suggests that Juan is losing money over time, which could imply that he is spending his savings rather than saving more.

Now let's evaluate the responses:

  1. Juan starts with $30 in savings and increases his savings amount by $1 each week.

    • This would mean his savings increase, which does not describe a graph that goes from $30 to $0. (Incorrect)

  2. Juan saves $30 per week.

    • This would mean Juan's savings would increase, starting from $30 and continuing to grow, which does not match the graph. (Incorrect)

  3. Juan starts with $30 in savings and increases his savings amount by $5 each week.

    • This again implies an increase in savings every week, which doesn't match the graph. (Incorrect)

  4. Juan starts with $5 in savings and increases his savings amount by $30 each week.

    • This also indicates an increase in savings, starting from a much lower point, leading to a growing amount, which does not match the graph. (Incorrect)

Given these options, none directly matches the description of a graph that starts with $30 and ends at $0 over a designated period. However, if the intent was for Juan to be spending money instead of saving it, the options provided do not capture that scenario accurately.

If I had to deduce a potential answer, it might involve something related to Juan spending his savings rather than saving or increasing them. However, based on the provided options, none seem to be a correct match for the scenario described by the graph.