Math Problem Statement

Use the graph of the function to find its domain and range. Write the domain and range in interval notation.

Solution

Looking at the graph, we can analyze the domain and range of the function.

Domain:

The domain represents the set of all possible x-values for which the function is defined. From the graph, it appears that the graph starts at x=7x = -7 and goes indefinitely to the right. Thus, the domain of the function is:

Domain: [7,)\text{Domain: } [-7, \infty)

Range:

The range represents the set of all possible y-values. From the graph, the function reaches down to y=7y = -7 and continues to increase upwards without bound. Thus, the range of the function is:

Range: [7,)\text{Range: } [-7, \infty)

Final Answer:

  • Domain: [7,)[-7, \infty)
  • Range: [7,)[-7, \infty)

Would you like more details or clarifications?

Here are five related questions to deepen your understanding:

  1. How do you determine the domain of a function if no graph is given?
  2. Can a function's range be limited if the domain is unlimited?
  3. How would the domain change if there was a vertical asymptote in the graph?
  4. What would the range be if the function had a horizontal asymptote at y=5y = 5?
  5. How do you express domain and range for functions with jumps or holes?

Tip: Always check for asymptotes or undefined points when determining domain and range from a graph.

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Math Problem Analysis

Mathematical Concepts

Domain and Range
Functions
Graph Analysis

Formulas

Interval notation for domain and range

Theorems

Basic function behavior from graph interpretation

Suitable Grade Level

Grades 9-11