Math Problem Statement

Estimate the domain and range of the function 𝑦=𝑓(π‘₯) graphed to the right. Assume the entire graph is shown.

(a) What is the domain of 𝑓(π‘₯) ?

(b) What is the range of 𝑓(π‘₯) ?

Estimate the domain and range of the function y = f(x) graphed to the right. Assume the entire graph is shown. (a) What is the domain of f(x)? (b) What is the range of f(x)?

Solution

Let's analyze the graph you've uploaded to estimate the domain and range of the function y=f(x)y = f(x).

(a) Domain of f(x)f(x):

The domain refers to the set of all possible xx-values for which the function is defined. From the graph, we can estimate the horizontal extent of the function.

  • The leftmost point of the graph appears to be at x=βˆ’6x = -6.
  • The rightmost point of the graph appears to be at x=6x = 6.

Thus, the domain of the function is approximately:

Domain=[βˆ’6,6]\text{Domain} = [-6, 6]

(b) Range of f(x)f(x):

The range refers to the set of all possible yy-values that the function takes. From the graph, we can estimate the vertical extent of the function.

  • The lowest point on the graph appears to be at y=βˆ’9y = -9.
  • The highest point on the graph appears to be at y=9y = 9.

Thus, the range of the function is approximately:

Range=[βˆ’9,9]\text{Range} = [-9, 9]

Would you like more details on how these values were estimated? Let me know if you have questions.

Further Questions:

  1. How does the slope of each line segment influence the behavior of the function?
  2. What can you say about the continuity of the function based on the graph?
  3. Are there any gaps in the graph? How do they affect the function?
  4. How would the domain and range change if the graph was extended further?
  5. Can you describe the intercepts of the function based on the graph?

Tip:

When estimating domain and range, always look for the horizontal and vertical boundaries of the graph to define the limits of xx and yy.

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Math Problem Analysis

Mathematical Concepts

Functions
Domain and Range
Coordinate Geometry

Formulas

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Theorems

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Suitable Grade Level

Grades 8-10