Answered

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Consider the function represented by the equation [tex]$x - y = 3[tex]$[/tex]. What is the equation written in function notation, with [tex]$[/tex]x$[/tex] as the independent variable?

A. [tex]$f(x) = y + 3$[/tex]
B. [tex]$f(x) = -y - 3$[/tex]
C. [tex]$f(x) = -x + 3$[/tex]
D. [tex]$f(x) = x - 3$[/tex]

Sagot :

GinnyAnswer
To rewrite the given equation \( x - y = 3 \) in function notation with \( x \) as the independent variable, follow these steps:

1. Start with the given equation:
[tex]\[ x - y = 3 \][/tex]

2. Solve for \( y \):
[tex]\[ -y = 3 - x \][/tex]

3. Multiply both sides by \( -1 \) to isolate \( y \):
[tex]\[ y = x - 3 \][/tex]

4. To express this as a function \( f(x) \), we write:
[tex]\[ f(x) = x - 3 \][/tex]

Among the given multiple-choice options:
a) \( f(x) = y + 3 \)
b) \( f(x) = -y - 3 \)
c) \( f(x) = -x + 3 \)
d) \( f(x) = x - 3 \)

The correct answer is:
[tex]\[ \boxed{f(x) = x - 3} \][/tex]
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