Math Problem Statement

Yes or no

Do the table and the graph represent the same function?

Solution

To determine whether the table and the graph represent the same function, we need to check if the points from the table align with the graph.

Given Table:

x-valuey-value
25-1405
30-1660
35-1825
40-1900
45-2155

Observing the Graph:

  • The graph shows a decreasing trend, which aligns with the negative slope seen in the table values.
  • The y-values in the table decrease as x increases, which also matches the downward trend in the graph.
  • Checking specific values visually, the plotted points seem to align with those in the table.

Since the table values appear to match the trend of the graph, the correct answer is "Yes".

Would you like a more detailed verification using an equation?

Here are five related questions you might find useful:

  1. How do you determine if a function is linear from a table?
  2. What are some methods to verify if a table and a graph match?
  3. How do you find the equation of a function given a table of values?
  4. What is the significance of the slope in a function's graph?
  5. How can graphing software help in verifying mathematical relationships?

Tip:

To verify a function, check if the differences between y-values remain consistent for equal x-intervals (for a linear function).

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Math Problem Analysis

Mathematical Concepts

Linear functions
Graph analysis
Data table interpretation

Formulas

Slope formula (m = (y2 - y1) / (x2 - x1))

Theorems

Concept of linearity in functions

Suitable Grade Level

Grades 8-10