Which functions are decreasing?

Select all answers that are correct.

Responses

The function goes through begin ordered pair 2 comma 8 end ordered pair, begin ordered pair 2.5 comma 2 end ordered pair, begin ordered pair 4 comma 0.5 end ordered pair, and begin ordered pair 6 comma 0.2 end ordered pair.
Image with alt text: The function goes through begin ordered pair 2 comma 8 end ordered pair, begin ordered pair 2.5 comma 2 end ordered pair, begin ordered pair 4 comma 0.5 end ordered pair, and begin ordered pair 6 comma 0.2 end ordered pair.

The function goes through begin ordered pair negative 4 comma negative 2.5 end ordered pair, begin ordered pair negative 3 comma negative 5 end ordered pair, begin ordered pair negative 2 comma negative 2 end ordered pair, begin ordered pair 0 comma 5 end ordered pair, begin ordered pair 2 comma negative 2 end ordered pair, begin ordered pair 3 comma negative 5 end ordered pair and begin ordered pair 4 comma negative 2.5 end ordered pair.
Image with alt text: The function goes through begin ordered pair negative 4 comma negative 2.5 end ordered pair, begin ordered pair negative 3 comma negative 5 end ordered pair, begin ordered pair negative 2 comma negative 2 end ordered pair, begin ordered pair 0 comma 5 end ordered pair, begin ordered pair 2 comma negative 2 end ordered pair, begin ordered pair 3 comma negative 5 end ordered pair and begin ordered pair 4 comma negative 2.5 end ordered pair.

The function consists of four sections. Section 1 is a line from begin ordered pair negative 3 comma 4 end ordered pair to begin ordered pair negative 1 comma 4 end ordered pair. Section 2 is a line from begin ordered pair negative 1 comma 4 end ordered pair to begin ordered pair 1 comma 0 end ordered pair. Section 3 is a line from begin ordered pair 1 comma 0 end ordered pair to begin ordered pair 3 comma 2 end ordered pair. Section 4 is a line from begin ordered pair 3 comma 2 end ordered pair to begin ordered pair 5 comma negative 2 end ordered pair.
Image with alt text: The function consists of four sections. Section 1 is a line from begin ordered pair negative 3 comma 4 end ordered pair to begin ordered pair negative 1 comma 4 end ordered pair. Section 2 is a line from begin ordered pair negative 1 comma 4 end ordered pair to begin ordered pair 1 comma 0 end ordered pair. Section 3 is a line from begin ordered pair 1 comma 0 end ordered pair to begin ordered pair 3 comma 2 end ordered pair. Section 4 is a line from begin ordered pair 3 comma 2 end ordered pair to begin ordered pair 5 comma negative 2 end ordered pair.

The function consists of four sections. Section 1 is a line from begin ordered pair negative 5 comma 2 end ordered pair to begin ordered pair negative 2 comma 2 end ordered pair. Section 2 is a line from begin ordered pair negative 2 comma 2 end ordered pair to begin ordered pair 1 comma 4 end ordered pair. Section 3 is a line from begin ordered pair 1 comma 4 end ordered pair to begin ordered pair 3 comma 4 end ordered pair. Section 4 is a line from begin ordered pair 3 comma 4 end ordered pair to begin ordered pair 5 comma 1 end ordered pair.

1 answer

To determine which functions are decreasing, we need to check the ordered pairs or the sections of each function for their trend as the x-values increase.

  1. First Function:

    • Points: (2, 8), (2.5, 2), (4, 0.5), (6, 0.2)
    • As x increases from 2 to 6, the y-values decrease from 8 to 0.2.
    • Decreasing: Yes.
  2. Second Function:

    • Points: (-4, -2.5), (-3, -5), (-2, -2), (0, 5), (2, -2), (3, -5), (4, -2.5)
    • As x increases from -4 to 4, the y-values do not consistently decrease (they go from -2.5 to -5, then back to 5, then decrease again to -2, and then drop to -5).
    • Decreasing: No.
  3. Third Function:

    • Section 1: (-3, 4) to (-1, 4) → y remains constant.
    • Section 2: (-1, 4) to (1, 0) → y decreases.
    • Section 3: (1, 0) to (3, 2) → y increases.
    • Section 4: (3, 2) to (5, -2) → y decreases.
    • Overall, there are increasing sections, so it's not strictly decreasing.
    • Decreasing: No.
  4. Fourth Function:

    • Section 1: (-5, 2) to (-2, 2) → y remains constant.
    • Section 2: (-2, 2) to (1, 4) → y increases.
    • Section 3: (1, 4) to (3, 4) → y remains constant.
    • Section 4: (3, 4) to (5, 1) → y decreases.
    • Again, there are increasing sections, so it’s not strictly decreasing.
    • Decreasing: No.

Based on the analysis, the only function that is strictly decreasing is the First Function. Thus, the correct response is:

  • The first function.