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f(x) = -5x + 2

f(x) = -5x + 2

Algebra and Trigonometry (6th Edition)
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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Find the indicated value of each function.

(a) f(0)

(b) f(3)

(c) f(-2)

### Understanding Linear Functions: Example Problem **Problem 55:** Given the linear function \( f(x) = -5x + 2 \). #### Explanation: This expression represents a linear function where: - The coefficient of \( x \) is \(-5\), which indicates the slope of the line. A negative slope means the line will decrease as it moves from left to right on a graph. - The constant term is \(2\), which represents the y-intercept. This is the point where the line crosses the y-axis. #### Graphical Representation: A graph of this function would consist of a straight line with the following characteristics: - **Slope**: \(-5\), so the line falls steeply as \( x \) increases. - **Y-Intercept**: \(2\), meaning the line crosses the y-axis at this point. To graph this function: 1. Start at the y-intercept (0, 2). 2. Use the slope to find another point. From (0, 2), move down 5 units and 1 unit to the right to arrive at the point (1, -3). 3. Draw a straight line through these points to complete the graph. This function models relationships where there is a consistent decrease by 5 units in \( f(x) \) for every 1 unit increase in \( x \).
Transcribed Image Text:### Understanding Linear Functions: Example Problem **Problem 55:** Given the linear function \( f(x) = -5x + 2 \). #### Explanation: This expression represents a linear function where: - The coefficient of \( x \) is \(-5\), which indicates the slope of the line. A negative slope means the line will decrease as it moves from left to right on a graph. - The constant term is \(2\), which represents the y-intercept. This is the point where the line crosses the y-axis. #### Graphical Representation: A graph of this function would consist of a straight line with the following characteristics: - **Slope**: \(-5\), so the line falls steeply as \( x \) increases. - **Y-Intercept**: \(2\), meaning the line crosses the y-axis at this point. To graph this function: 1. Start at the y-intercept (0, 2). 2. Use the slope to find another point. From (0, 2), move down 5 units and 1 unit to the right to arrive at the point (1, -3). 3. Draw a straight line through these points to complete the graph. This function models relationships where there is a consistent decrease by 5 units in \( f(x) \) for every 1 unit increase in \( x \).
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