Math Problem Statement

Determine the range of the following graph:

Solution

To determine the range of the given graph, we need to identify the lowest and highest points along the yy-axis that the graph reaches.

Looking at the graph:

  • The lowest point on the graph occurs near y=8y = -8, which appears to be the minimum value the graph reaches.
  • The highest point occurs at y=10y = 10, which is the maximum value reached by the graph.

Since the graph includes these extreme values (both the minimum and maximum are shown as closed circles), the range of the function is:

[8,10]\boxed{[-8, 10]}

Let me know if you want more details or if you have any questions!

Here are 5 follow-up questions you might find interesting:

  1. What is the domain of this graph?
  2. How do you determine if the graph represents a function?
  3. Can this graph represent a polynomial function? If so, of what degree?
  4. How can we estimate the turning points of this graph?
  5. What role do the end behaviors play in determining the range of a graph?

Tip: The range of a function refers to all possible output values (y-values), while the domain refers to all possible input values (x-values).

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Math Problem Analysis

Mathematical Concepts

Functions
Range of a Function

Formulas

-

Theorems

Range of a Function

Suitable Grade Level

Grades 8-10