Math Problem Statement

Analyze a table showing a home’s electric bill B in dollars given the average monthly temperature t in Phoenix, and determine input/output variables, practical domain, and practical range.

Solution

The image shows a page from a student book related to functions, specifically focusing on input/output variables, domain, and range. There is a table of values depicting a home's electric bill BB in dollars in relation to the average monthly temperature tt in Phoenix (in degrees Fahrenheit). Additionally, there is a graph, but it is somewhat unclear due to the image quality.

To analyze the information presented:

1. Input/Output and Variables:

  • Input: Temperature (tt) in degrees Fahrenheit.
  • Output: Electric bill (BB) in dollars.

2. Practical Domain:

The domain would include the range of temperatures listed in the table: {55F,60F,65F,73F,82F,91F,95F,77F,88F,64F}\{55^\circ F, 60^\circ F, 65^\circ F, 73^\circ F, 82^\circ F, 91^\circ F, 95^\circ F, 77^\circ F, 88^\circ F, 64^\circ F\} This gives the minimum and maximum temperatures: 55Ft95F55^\circ F \leq t \leq 95^\circ F

3. Practical Range:

The range includes the corresponding electric bills from the table: {125,115,98,102,180,185,188,122,115,125}\{125, 115, 98, 102, 180, 185, 188, 122, 115, 125 \} The minimum and maximum electric bills: 98B18898 \leq B \leq 188


Would you like to dive deeper into any specific part, or explore further details like how to determine trends or interpret the graph?

Here are some related questions:

  1. What type of function might represent the relationship between tt and BB?
  2. How does temperature affect the electric bill based on the given table?
  3. Can the data be used to make predictions about electric bills at temperatures not listed?
  4. Is the relationship between temperature and the electric bill linear or non-linear?
  5. How would you calculate the average electric bill based on the given data?

Tip: When analyzing a table, always check for patterns or changes between inputs and outputs to hypothesize the relationship (linear, quadratic, etc.).

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Math Problem Analysis

Mathematical Concepts

Functions
Input/Output Variables
Domain
Range

Formulas

None provided, but concepts include identifying practical domain and range from a table.

Theorems

None explicitly involved; related to function analysis.

Suitable Grade Level

Grades 9-11