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If function [tex]g[/tex] is defined by the equation [tex]y - 3x = -14[/tex], which equation represents the function in function notation?

A. [tex]g(x) = 3x - 14[/tex]
B. [tex]g(x) = -3x - 14[/tex]
C. [tex]g(x) = 3x + 14[/tex]
D. [tex]g(x) = -3x + 14[/tex]

Sagot :

GinnyAnswer
To convert the equation [tex]\( y - 3x = -14 \)[/tex] to function notation [tex]\( g(x) \)[/tex], we need to solve for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex].

Here are the steps to do so:

1. Start with the given equation:
[tex]\[ y - 3x = -14 \][/tex]

2. Solve for [tex]\( y \)[/tex] by isolating it on one side of the equation. To do this, add [tex]\( 3x \)[/tex] to both sides of the equation:
[tex]\[ y - 3x + 3x = -14 + 3x \][/tex]
Simplifying, we obtain:
[tex]\[ y = 3x - 14 \][/tex]

Now that we have [tex]\( y \)[/tex] expressed in terms of [tex]\( x \)[/tex], we can write the function notation [tex]\( g(x) \)[/tex]:
[tex]\[ g(x) = 3x - 14 \][/tex]

The correct function notation is [tex]\( g(x) = 3x - 14 \)[/tex], which corresponds to:

A. [tex]\( g(x) = 3x - 14 \)[/tex]

So, the correct answer is:

A. [tex]\( g(x) = 3x - 14 \)[/tex]
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