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Calculus: Early Transcendentals
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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Click to choose the correct graph to match the given expression.

y = x 2 - 2x

### Graph Descriptions #### Graph 1: - **Type**: Linear Function - **Description**: This graph depicts a continuous line with a positive slope. The line moves from the bottom left to the top right. It passes through the origin and has an open circle at \(x = -2\), indicating that the value at that point is not included in the solution set. #### Graph 2: - **Type**: Quadratic Function - **Description**: This graph represents a parabola opening upwards. The vertex is at approximately \((-1, -3)\). The parabola is continuous but has an open circle at \(x = 2\), showing that it does not include the point where the parabola would normally sit, implying a discontinuity at that point. #### Graph 3: - **Type**: Piecewise Function - **Description**: This graph is a combination of a horizontal line and a diagonal segment. From \(x = -5\) to \(x = 2\), the graph is a horizontal line at \(y = 2\) with an open circle at \(x = 2\). From \(x = 2\) onwards, the line ascends with a positive slope, moving to the right. These two sections are distinct segments of the complete function. #### Graph 4: - **Type**: Exponential Function - **Description**: Illustrated here is a curve that increases rapidly. Beginning from a low y-value, the graph rises steeply as x increases, especially noticeable after \(x = -2\). The curve appears continuous and does not intersect the x-axis.
Transcribed Image Text:### Graph Descriptions #### Graph 1: - **Type**: Linear Function - **Description**: This graph depicts a continuous line with a positive slope. The line moves from the bottom left to the top right. It passes through the origin and has an open circle at \(x = -2\), indicating that the value at that point is not included in the solution set. #### Graph 2: - **Type**: Quadratic Function - **Description**: This graph represents a parabola opening upwards. The vertex is at approximately \((-1, -3)\). The parabola is continuous but has an open circle at \(x = 2\), showing that it does not include the point where the parabola would normally sit, implying a discontinuity at that point. #### Graph 3: - **Type**: Piecewise Function - **Description**: This graph is a combination of a horizontal line and a diagonal segment. From \(x = -5\) to \(x = 2\), the graph is a horizontal line at \(y = 2\) with an open circle at \(x = 2\). From \(x = 2\) onwards, the line ascends with a positive slope, moving to the right. These two sections are distinct segments of the complete function. #### Graph 4: - **Type**: Exponential Function - **Description**: Illustrated here is a curve that increases rapidly. Beginning from a low y-value, the graph rises steeply as x increases, especially noticeable after \(x = -2\). The curve appears continuous and does not intersect the x-axis.
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