Math Problem Statement

Determine the range of the following graph.

Solution

The graph shows a curve where we are tasked with determining the range of the function. The range is the set of all possible yy-values that the function can take.

Observing the graph:

  1. The lowest point on the graph appears to be y=10y = -10.
  2. The highest point on the graph appears to be y=2y = -2.

Range:

The yy-values span from 10-10 to 2-2, inclusive. Therefore, the range of the function is: [10,2][-10, -2]

Would you like a step-by-step explanation of how I analyzed the graph, or do you have more questions? Here are 5 related questions to expand your understanding:

  1. What is the domain of this graph?
  2. How do you find the range for graphs that extend infinitely?
  3. How can you determine if a graph has a restricted range?
  4. What are examples of functions with limited ranges?
  5. How does the range differ between quadratic and cubic functions?

Tip: Always check for any open or closed circles on the graph to determine if endpoints are included in the range.

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Math Problem Analysis

Mathematical Concepts

Range of a function
Graph analysis

Formulas

Range: Set of all possible y-values

Theorems

Understanding of the range from a graph

Suitable Grade Level

Grades 8-10