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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Given the graph of the function f(x) shown below, solve the inequalities. Express your answer as an inequality.
![Given the graph of the function \( f(x) \) shown below, solve the inequalities. Express your answer as an inequality.
### Graph Description
The graph is a Cartesian coordinate plane with a red line representing the function \( f(x) \). The line intersects the y-axis at \((0, -4)\) and passes through the point \((2, 0)\), forming a linear graph with a positive slope.
The x-values range from -15 to 15, and the y-values also range from -15 to 15. The slope of the line can be calculated using the points provided: \((0, -4)\) and \((2, 0)\).
### Solve the Inequalities
a. \( f(x) < 8 \) if \[ \_\_\_\_\_\_ \]
b. \( f(x) > 8 \) if \[ \_\_\_\_\_\_ \]
c. \( f(x) = 8 \) if \[ \_\_\_\_\_\_ \]
### Explanation of the Linear Function
- **Line Equation**: Using the slope-intercept form \( y = mx + b \), the slope \( m \) can be calculated as:
\[
m = \frac{0 - (-4)}{2 - 0} = 2
\]
Thus, the equation of the line is \( y = 2x - 4 \).
- **Solving for \( f(x) = 8 \)**:
\[
2x - 4 = 8 \\
2x = 12 \\
x = 6
\]
Therefore, \( f(x) = 8 \) if \( x = 6 \).
- **Solving for \( f(x) < 8 \)**:
\[
2x - 4 < 8 \\
2x < 12 \\
x < 6
\]
Therefore, \( f(x) < 8 \) if \( x < 6 \).
- **Solving for \( f(x) > 8 \)**:
\[
2x - 4 > 8 \\
2x > 12 \\
x > 6
\]
Therefore, \( f(x) > 8 \) if \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9608159c-84a5-4f71-a9c8-653300d0efd9%2Fdd14ae79-6bc9-47f6-bac5-50695e9e35bc%2Fp0i1h8m_processed.png&w=3840&q=75)
Transcribed Image Text:Given the graph of the function \( f(x) \) shown below, solve the inequalities. Express your answer as an inequality.
### Graph Description
The graph is a Cartesian coordinate plane with a red line representing the function \( f(x) \). The line intersects the y-axis at \((0, -4)\) and passes through the point \((2, 0)\), forming a linear graph with a positive slope.
The x-values range from -15 to 15, and the y-values also range from -15 to 15. The slope of the line can be calculated using the points provided: \((0, -4)\) and \((2, 0)\).
### Solve the Inequalities
a. \( f(x) < 8 \) if \[ \_\_\_\_\_\_ \]
b. \( f(x) > 8 \) if \[ \_\_\_\_\_\_ \]
c. \( f(x) = 8 \) if \[ \_\_\_\_\_\_ \]
### Explanation of the Linear Function
- **Line Equation**: Using the slope-intercept form \( y = mx + b \), the slope \( m \) can be calculated as:
\[
m = \frac{0 - (-4)}{2 - 0} = 2
\]
Thus, the equation of the line is \( y = 2x - 4 \).
- **Solving for \( f(x) = 8 \)**:
\[
2x - 4 = 8 \\
2x = 12 \\
x = 6
\]
Therefore, \( f(x) = 8 \) if \( x = 6 \).
- **Solving for \( f(x) < 8 \)**:
\[
2x - 4 < 8 \\
2x < 12 \\
x < 6
\]
Therefore, \( f(x) < 8 \) if \( x < 6 \).
- **Solving for \( f(x) > 8 \)**:
\[
2x - 4 > 8 \\
2x > 12 \\
x > 6
\]
Therefore, \( f(x) > 8 \) if \(
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