Ask a New Question
Menu

What is the rate of change of the function represented by the table?xy1-7.52-63-4.54-3NOTE: In the bottom right corner of each question, you will see an option to check answer. Click this to check your answer before moving on to the next question. It will not tell you the correct answer, but it will tell you if the answer you selected is correct. You can use this feature twice per question.(1 point)Responses1.51.5-1.5-1.5-2.5-2.52.52.5Skip to navigation

1 answer

To find the rate of change of the function represented by the table, you can use the formula for the slope between two points:

\[ \text{Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1} \]

Let's calculate this for the pairs of points provided in the table (assumed as pairs based on the x-y values you provided).

From the table, the points appear to be:

  • \( (1, -7.5) \)
  • \( (2, -6) \)
  • \( (3, -4.5) \)
  • \( (4, -3) \)

Let's calculate the rate of change between consecutive points.

  1. Between \( (1, -7.5) \) and \( (2, -6) \):

\[ \text{Rate of Change} = \frac{-6 - (-7.5)}{2 - 1} = \frac{-6 + 7.5}{1} = \frac{1.5}{1} = 1.5 \]

  1. Between \( (2, -6) \) and \( (3, -4.5) \):

\[ \text{Rate of Change} = \frac{-4.5 - (-6)}{3 - 2} = \frac{-4.5 + 6}{1} = \frac{1.5}{1} = 1.5 \]

  1. Between \( (3, -4.5) \) and \( (4, -3) \):

\[ \text{Rate of Change} = \frac{-3 - (-4.5)}{4 - 3} = \frac{-3 + 4.5}{1} = \frac{1.5}{1} = 1.5 \]

Since the rate of change is consistent at \( 1.5 \) for each interval, we can conclude that the rate of change of the function represented by the table is \( 1.5 \).

Based on your options, you would choose:

1.5.