Math Problem Statement

Find the domain, range, and specific function values based on the graph of the function f(x).

Solution

Let's analyze the graph of the function f(x)f(x) step by step and solve the questions:

  1. Find the domain, using interval notation: The domain refers to all the possible xx-values where the function is defined. From the graph, the function extends from x=4x = -4 to x=4x = 4, inclusive of these values. Thus, the domain is: Domain=[4,4]\text{Domain} = [-4, 4]

  2. Find the range, using interval notation: The range refers to all the possible yy-values the function can take. From the graph, the function goes as low as y=4y = -4 (at x=1x = -1) and as high as y=9y = 9 (at x=3.5x = -3.5). Thus, the range is: Range=[4,9]\text{Range} = [-4, 9]

  3. Determine f(0)f(0): From the graph, when x=0x = 0, the corresponding yy-value is 2-2. Therefore: f(0)=2f(0) = -2

  4. Determine f(4)f(4): From the graph, when x=4x = 4, the corresponding yy-value is 22. Therefore: f(4)=2f(4) = 2

  5. Determine the value of xx where f(x)=4f(x) = -4: From the graph, the function equals 4-4 at x=1x = -1. Therefore: x=1x = -1

Summary of Answers:

  1. Domain: [4,4][-4, 4]
  2. Range: [4,9][-4, 9]
  3. f(0)=2f(0) = -2
  4. f(4)=2f(4) = 2
  5. x=1x = -1 where f(x)=4f(x) = -4

Would you like further details or clarifications?

Here are five related questions for further practice:

  1. What is the value of f(4)f(-4)?
  2. How many x-intercepts does the function have?
  3. Determine the local maximum and minimum points.
  4. Is the function even, odd, or neither?
  5. Find all values of xx where f(x)=0f(x) = 0.

Tip: When interpreting a graph, always check how the curve behaves at the endpoints and key points, as these often determine domain, range, and critical points.

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Math Problem Analysis

Mathematical Concepts

Function Analysis
Graph Interpretation
Domain and Range

Formulas

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Theorems

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Suitable Grade Level

Grades 9-11