4. Use the graph of f to answer the questions below: 4 3 2 -4-3-2-11 -2- -3 -4 y 1 2 3 4 X (a) What is the domain of f? (b) What is the range of f? (c) What is the value of f(0)? (d) What is the value of f(3)?

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Graph Analysis for Function \( f \)**

The graph represents a function \( f \) plotted on a coordinate system. The x-axis is labeled from -4 to 4, and the y-axis is labeled from -4 to 4. Here's a detailed explanation of the graph and the accompanying questions:

- **Graph Description:**
  - The function begins at approximately \((-3, 1)\) with a closed dot, indicating that this point is included in the graph.
  - The function is drawn with a curve extending to the right and upwards.
  - The graph ends at approximately \((2, 3)\) with an open dot, indicating this point is not included in the graph.

- **Questions and Analysis:**

  (a) **What is the domain of \( f \)?**
  - The domain is the set of all possible x-values. From the graph, the function starts at \(x = -3\) and ends at \(x = 2\). Thus, the domain is \([-3, 2)\).

  (b) **What is the range of \( f \)?**
  - The range is the set of all possible y-values. From the graph, the y-values start at 1 and go up to 3 (not including 3). Thus, the range is \([1, 3)\).

  (c) **What is the value of \( f(0) \)?**
  - To find \( f(0) \), locate \(x = 0\) on the graph. From the function curve, \( f(0) = 2\).

  (d) **What is the value of \( f(3) \)?**
  - Since \(x = 3\) is not in the domain of the function (the domain ends at 2), \( f(3) \) is not defined.
Transcribed Image Text:**Graph Analysis for Function \( f \)** The graph represents a function \( f \) plotted on a coordinate system. The x-axis is labeled from -4 to 4, and the y-axis is labeled from -4 to 4. Here's a detailed explanation of the graph and the accompanying questions: - **Graph Description:** - The function begins at approximately \((-3, 1)\) with a closed dot, indicating that this point is included in the graph. - The function is drawn with a curve extending to the right and upwards. - The graph ends at approximately \((2, 3)\) with an open dot, indicating this point is not included in the graph. - **Questions and Analysis:** (a) **What is the domain of \( f \)?** - The domain is the set of all possible x-values. From the graph, the function starts at \(x = -3\) and ends at \(x = 2\). Thus, the domain is \([-3, 2)\). (b) **What is the range of \( f \)?** - The range is the set of all possible y-values. From the graph, the y-values start at 1 and go up to 3 (not including 3). Thus, the range is \([1, 3)\). (c) **What is the value of \( f(0) \)?** - To find \( f(0) \), locate \(x = 0\) on the graph. From the function curve, \( f(0) = 2\). (d) **What is the value of \( f(3) \)?** - Since \(x = 3\) is not in the domain of the function (the domain ends at 2), \( f(3) \) is not defined.
Expert Solution
Step 1

 From the given graph.

To find 

(a) The domain of f

(b) The range of f

(c) The value of f(0)

(d) The value of f(3)

Explanation:

Domain:

It is the set of values of x where the function is defined.

Range:

It is the set of values of y that the function assumes for each x in its domain.

 

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