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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![### Determine Whether the Equation Defines \( y \) as a Function of \( x \)
Consider the given equation:
\[ 4x - 8y = 2 \]
#### Choose the Correct Option:
- \( \circ \) is a function
- \( \circ \) is not a function
**Explanation:**
To determine whether the equation defines \( y \) as a function of \( x \), isolate \( y \) on one side of the equation. This helps reveal whether each \( x \) value will produce a unique \( y \) value.
The original equation is:
\[ 4x - 8y = 2 \]
Rearrange the equation to solve for \( y \):
\[ -8y = 2 - 4x \]
\[ y = \frac{2 - 4x}{-8} \]
\[ y = \frac{-4x + 2}{-8} \]
\[ y = \frac{4x}{8} - \frac{2}{8} \]
\[ y = \frac{x}{2} - \frac{1}{4} \]
Now \( y \) is expressed as:
\[ y = \frac{1}{2}x - \frac{1}{4} \]
This is a linear equation in slope-intercept form, where \( y \) is explicitly defined in terms of \( x \). This indicates that for each value of \( x \), there is exactly one corresponding value of \( y \).
So, the equation *is* a function.
#### Choose the Correct Option:
- \( \bullet \) is a function
- \( \circ \) is not a function](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F429fd668-1075-4973-8e47-64e8dad266df%2Fa58f002b-aa05-4de5-ba67-1ed537578449%2F9w8f83p_processed.png&w=3840&q=75)
Transcribed Image Text:### Determine Whether the Equation Defines \( y \) as a Function of \( x \)
Consider the given equation:
\[ 4x - 8y = 2 \]
#### Choose the Correct Option:
- \( \circ \) is a function
- \( \circ \) is not a function
**Explanation:**
To determine whether the equation defines \( y \) as a function of \( x \), isolate \( y \) on one side of the equation. This helps reveal whether each \( x \) value will produce a unique \( y \) value.
The original equation is:
\[ 4x - 8y = 2 \]
Rearrange the equation to solve for \( y \):
\[ -8y = 2 - 4x \]
\[ y = \frac{2 - 4x}{-8} \]
\[ y = \frac{-4x + 2}{-8} \]
\[ y = \frac{4x}{8} - \frac{2}{8} \]
\[ y = \frac{x}{2} - \frac{1}{4} \]
Now \( y \) is expressed as:
\[ y = \frac{1}{2}x - \frac{1}{4} \]
This is a linear equation in slope-intercept form, where \( y \) is explicitly defined in terms of \( x \). This indicates that for each value of \( x \), there is exactly one corresponding value of \( y \).
So, the equation *is* a function.
#### Choose the Correct Option:
- \( \bullet \) is a function
- \( \circ \) is not a function
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