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Ketch a graph of f(x) = 3 2 x + 2

Ketch a graph of f(x) = 3 2 x + 2

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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**Sketch a Graph of \( f(x) = \frac{3}{2}x + 2 \)** The image presents the equation of a linear function \( f(x) = \frac{3}{2}x + 2 \) and includes a coordinate plane with both x and y axes ranging from -5 to 5. ### Key Components: 1. **Equation**: The given equation is \( f(x) = \frac{3}{2}x + 2 \), which is in the slope-intercept form \( y = mx + b \), where \( m \) represents the slope and \( b \) represents the y-intercept. 2. **Coordinate Grid**: - The x-axis and y-axis both span from -5 to 5. - The grid is drawn in a standard Cartesian plane format with horizontal and vertical lines marking intervals of 1 unit. 3. **Graphing Tools**: Below the coordinate plane, there are options to draw various types of graphs and objects: - Linear function (highlighted) - Quadratic function - Piecewise function - Circle - Point indicator - There is also a "Clear All" button to reset the graph. ### Step-by-Step Graphing Explanation: 1. **Identify the y-intercept**: - The y-intercept \( b \) is 2. This tells us that the point (0, 2) is on the graph. You can plot this point on the y-axis where y is 2. 2. **Determine the slope**: - The slope \( m \) is \( \frac{3}{2} \). This means for every 2 units you move right along the x-axis, you move up 3 units along the y-axis. 3. **Plot Additional Points Using the Slope**: - From the y-intercept (0, 2), move 2 units right to x = 2, then move up 3 units (y + 3), which leads to the point (2, 5). - Alternatively, for every 2 units you move left along the x-axis, you move down 3 units along the y-axis, leading to other points such as (-2, -1). 4. **Draw the Line**: - Once you have plotted several points, draw a straight line through these points to represent the
Transcribed Image Text:**Sketch a Graph of \( f(x) = \frac{3}{2}x + 2 \)** The image presents the equation of a linear function \( f(x) = \frac{3}{2}x + 2 \) and includes a coordinate plane with both x and y axes ranging from -5 to 5. ### Key Components: 1. **Equation**: The given equation is \( f(x) = \frac{3}{2}x + 2 \), which is in the slope-intercept form \( y = mx + b \), where \( m \) represents the slope and \( b \) represents the y-intercept. 2. **Coordinate Grid**: - The x-axis and y-axis both span from -5 to 5. - The grid is drawn in a standard Cartesian plane format with horizontal and vertical lines marking intervals of 1 unit. 3. **Graphing Tools**: Below the coordinate plane, there are options to draw various types of graphs and objects: - Linear function (highlighted) - Quadratic function - Piecewise function - Circle - Point indicator - There is also a "Clear All" button to reset the graph. ### Step-by-Step Graphing Explanation: 1. **Identify the y-intercept**: - The y-intercept \( b \) is 2. This tells us that the point (0, 2) is on the graph. You can plot this point on the y-axis where y is 2. 2. **Determine the slope**: - The slope \( m \) is \( \frac{3}{2} \). This means for every 2 units you move right along the x-axis, you move up 3 units along the y-axis. 3. **Plot Additional Points Using the Slope**: - From the y-intercept (0, 2), move 2 units right to x = 2, then move up 3 units (y + 3), which leads to the point (2, 5). - Alternatively, for every 2 units you move left along the x-axis, you move down 3 units along the y-axis, leading to other points such as (-2, -1). 4. **Draw the Line**: - Once you have plotted several points, draw a straight line through these points to represent the
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