12 **Graph of a Function: Identifying Relative and Absolute Extrema**The image presents a graph of a function $ y = f(x) $. The task is to identify all the relative extrema (both relative maxima and minima) as well as the absolute extrema (the highest and lowest points over the entire domain of the function). ### Explanation of the GraphThe graph is a continuous curve plotted on a coordinate system with the x-axis ranging approximately from -4 to 5, and the y-axis ranging approximately from -6 to 6. The function appears to have several peaks and troughs.### Identifying Extrema- **Absolute Maximum:** The highest point on the graph.- **Absolute Minimum:** The lowest point on the graph.- **Relative Maximum:** A point where the function changes direction from increasing to decreasing.- **Relative Minimum:** A point where the function changes direction from decreasing to increasing.### Select the Correct ExtremaFrom the multiple-choice options given below, identify the correct extrema values for the function based on the graph.#### Options:a. Absolute Max (4,5); Absolute Min (2, -6); Relative Max’s (-1,2) and (4,5); Relative Mini’s (-3,-2) and (2,-6)b. Absolute Max (-4,5); Absolute Min (-2,-6); Relative Max’s (-1,2) and (4,5); Relative Mini’s (-3,-2) and (2,-6)c. Absolute Max (4,5); Absolute Min (2,-6); Relative Max’s (-1,2) and (4,5); Relative Mini’s (-3,-2) and (2,-6)d. Absolute Max (-4,-5); Absolute Min (-2,-6); Relative Max’s (-1,2) and (4,5); Relative Mini’s (-3,-2) and (2,-6)### Graph Details- **Maximum Points:** - (4, 5) - (-1, 2)- **Minimum Points:** - (2, -6) - (-3, -2)Correctly identifying these points involves analyzing where the curve peaks and dips. **Note:** Ensure accurate interpretation by carefully examining where the curve reaches its highest and lowest values.

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Below is the graph of a function y = f(x). Identify all the relative extrema and absolute extrema of the function. -3 -1 -1 3 -4 -2 -3 -4 -5 Select one: O a. Absolute Max (4,5); Absolute Min (2,-6); Relative Max's (-1,2) and (4,5); Relative Mini's (-3,-2) and (2,-6) O b. Absolute Max (-4,5); Absolute Min (-2,–6); Relative Max's (-1,2) and (4,5); Relative Mini's (-3,-2) and (2,-6) O c. Absolute Max (4,5); Absolute Min (2,-6); Relative Max's (-1,2) and (4,5); Relative Mini's (3,-2) and (-2,-6) d. Absolute Max (-4,-5); Absolute Min (-2,-6); Relative Max's (-1,2) and (4,5); Relative Mini's (-3,-2) and (2,-6)

Below is the graph of a function y = f(x). Identify all the relative extrema and absolute extrema of the function. -3 -1 -1 3 -4 -2 -3 -4 -5 Select one: O a. Absolute Max (4,5); Absolute Min (2,-6); Relative Max's (-1,2) and (4,5); Relative Mini's (-3,-2) and (2,-6) O b. Absolute Max (-4,5); Absolute Min (-2,–6); Relative Max's (-1,2) and (4,5); Relative Mini's (-3,-2) and (2,-6) O c. Absolute Max (4,5); Absolute Min (2,-6); Relative Max's (-1,2) and (4,5); Relative Mini's (3,-2) and (-2,-6) d. Absolute Max (-4,-5); Absolute Min (-2,-6); Relative Max's (-1,2) and (4,5); Relative Mini's (-3,-2) and (2,-6)

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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**Graph of a Function: Identifying Relative and Absolute Extrema**

The image presents a graph of a function $ y = f(x) $. The task is to identify all the relative extrema (both relative maxima and minima) as well as the absolute extrema (the highest and lowest points over the entire domain of the function).

### Explanation of the Graph
The graph is a continuous curve plotted on a coordinate system with the x-axis ranging approximately from -4 to 5, and the y-axis ranging approximately from -6 to 6. The function appears to have several peaks and troughs.

### Identifying Extrema
- **Absolute Maximum:** The highest point on the graph.
- **Absolute Minimum:** The lowest point on the graph.
- **Relative Maximum:** A point where the function changes direction from increasing to decreasing.
- **Relative Minimum:** A point where the function changes direction from decreasing to increasing.

### Select the Correct Extrema
From the multiple-choice options given below, identify the correct extrema values for the function based on the graph.

#### Options:
a. Absolute Max (4,5); Absolute Min (2, -6); Relative Max’s (-1,2) and (4,5); Relative Mini’s (-3,-2) and (2,-6)

b. Absolute Max (-4,5); Absolute Min (-2,-6); Relative Max’s (-1,2) and (4,5); Relative Mini’s (-3,-2) and (2,-6)

c. Absolute Max (4,5); Absolute Min (2,-6); Relative Max’s (-1,2) and (4,5); Relative Mini’s (-3,-2) and (2,-6)

d. Absolute Max (-4,-5); Absolute Min (-2,-6); Relative Max’s (-1,2) and (4,5); Relative Mini’s (-3,-2) and (2,-6)

### Graph Details
- **Maximum Points:**
- (4, 5)
- (-1, 2)
- **Minimum Points:**
- (2, -6)
- (-3, -2)

Correctly identifying these points involves analyzing where the curve peaks and dips.

**Note:** Ensure accurate interpretation by carefully examining where the curve reaches its highest and lowest values.

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