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For each of the following, determine whether the equation defines y as a function of x. 4x + |₂| = 0 y = 8 |x| - 5 5 2 y 42/2 5 x = (y + 4)² - 9 = x Function Function Function O Function Not a function Not a function Not a function Not a function

For each of the following, determine whether the equation defines y as a function of x. 4x + |₂| = 0 y = 8 |x| - 5 5 2 y 42/2 5 x = (y + 4)² - 9 = x Function Function Function O Function Not a function Not a function Not a function Not a function

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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For each of the following, determine whether the equation defines \( y \) as a function of \( x \). 1. **Equation:** \( 4x + |y| = 0 \) - \( \bigcirc \) Function - \( \bigcirc \) Not a function 2. **Equation:** \( y = 8|x| - 5 \) - \( \bigcirc \) Function - \( \bigcirc \) Not a function 3. **Equation:** \( x = \frac{2y}{5} \) - \( \bigcirc \) Function - \( \bigcirc \) Not a function 4. **Equation:** \( (y + 4)^2 - 9 = x \) - \( \bigcirc \) Function - \( \bigcirc \) Not a function (Selected) Explanation of Equations: - **First equation ( \( 4x + |y| = 0 \) ):** This equation involves an absolute value of \( y \). When solving for \( y \), it may give multiple values for a single input \( x \), indicating it is likely **Not a function**. - **Second equation ( \( y = 8|x| - 5 \) ):** This equation defines \( y \) directly in terms of \( x \), involving the absolute value of \( x \), generally making it a **Function** since each \( x \) corresponds to exactly one \( y \). - **Third equation ( \( x = \frac{2y}{5} \) ):** This equation expresses \( x \) as a function of \( y \). To determine whether \( y \) can be expressed as a function of \( x \), we would need to solve for \( y \) explicitly and see if for each \( x \), there will be a unique \( y \). It might indicate it is **Not a function**. - **Fourth equation ( \( (y + 4)^2 - 9 = x \) ):** This involves a squared term of \( y \). Squaring generally leads to two potential values for \( y \) for a given \( x \), making it **Not a function**. In this exercise, you are to determine the nature of the relationship between \( y \) and \( x \) for these given equations.
Transcribed Image Text:For each of the following, determine whether the equation defines \( y \) as a function of \( x \). 1. **Equation:** \( 4x + |y| = 0 \) - \( \bigcirc \) Function - \( \bigcirc \) Not a function 2. **Equation:** \( y = 8|x| - 5 \) - \( \bigcirc \) Function - \( \bigcirc \) Not a function 3. **Equation:** \( x = \frac{2y}{5} \) - \( \bigcirc \) Function - \( \bigcirc \) Not a function 4. **Equation:** \( (y + 4)^2 - 9 = x \) - \( \bigcirc \) Function - \( \bigcirc \) Not a function (Selected) Explanation of Equations: - **First equation ( \( 4x + |y| = 0 \) ):** This equation involves an absolute value of \( y \). When solving for \( y \), it may give multiple values for a single input \( x \), indicating it is likely **Not a function**. - **Second equation ( \( y = 8|x| - 5 \) ):** This equation defines \( y \) directly in terms of \( x \), involving the absolute value of \( x \), generally making it a **Function** since each \( x \) corresponds to exactly one \( y \). - **Third equation ( \( x = \frac{2y}{5} \) ):** This equation expresses \( x \) as a function of \( y \). To determine whether \( y \) can be expressed as a function of \( x \), we would need to solve for \( y \) explicitly and see if for each \( x \), there will be a unique \( y \). It might indicate it is **Not a function**. - **Fourth equation ( \( (y + 4)^2 - 9 = x \) ):** This involves a squared term of \( y \). Squaring generally leads to two potential values for \( y \) for a given \( x \), making it **Not a function**. In this exercise, you are to determine the nature of the relationship between \( y \) and \( x \) for these given equations.
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