Graph of the Function f(x) 3x - 4 Over the Domain -2 ≤ x

The function f(x) 3x - 4 is a linear function, and its graph is a straight line. This article will explore the graph of this function over the specified domain, -2 ≤ x

Understanding the Function f(x) 3x - 4

The given function, f(x) 3x - 4, is a linear function. A linear function can be generalized as f(x) mx b, where m is the slope and b is the y-intercept. In this case, m 3 and b -4. This means that for each unit increase in x, the value of f(x) increases by 3 units. The y-intercept, where the line crosses the y-axis, is at f(0) 3*0 - 4 -4.

Steps to Graph f(x) 3x - 4 Over the Domain -2 ≤ x

1. Identify the Slope and Y-Intercept

The slope m is 3. This indicates a rise of 3 units for every 1 unit increase in x. The y-intercept is at (0, -4), where the line intersects the y-axis.

2. Calculate Function Values at the Endpoints of the Domain

For x -2:

f(-2) 3*(-2) - 4 -6 - 4 -10

For x 3 (exclusive as the domain is -2 ≤ x

f(3) 3*3 - 4 9 - 4 5

3. Plot the Points

Plot the points (-2, -10) and (3, 5) on a coordinate plane.

4. Draw the Line

Connect the points with a straight line, ensuring that the point (3, 5) is not included in the graph due to the open interval notation for the domain (i.e., the endpoint 3 is not included).

Graph Overview

The graph of f(x) 3x - 4 over the domain -2 ≤ x

Domain, Endpoints, and Slope Summary

Domain: -2 ≤ x Endpoints: Open circle at (-2, -10) and the point (3, 5) is not included. Slope: 3, indicating a steep line that rises sharply.

Visual Representation

While I can't create visuals directly, you can sketch the graph based on the points and description provided. If you have graphing software or graph paper, plot the two points (-2, -10) and (3, 5) and draw the line between them, ensuring to leave an open circle at the point (3, 5) to represent the exclusive domain.

Mathematically: The function f(x) 3x - 4 can be described as a line segment between the points A(-2, -10) and B(3, 5).

Note: The domain restriction -2 ≤ x

By understanding these key aspects, you can effectively graph and analyze the function f(x) 3x - 4 over the specified domain.