Respuesta :
Answer:
4. [tex] x = 3y^2 [\tex]
Step-by-step explanation:
For an equation to be considered a function, there must be only one possible y-value for each value of x. That is, every x-value should have at exactly one y-value.
The equation, [tex] x = 3y^2 [\tex], is not a function, because there would be two possible values of y for any given x-value.
For example, let's say the x value given is 12.
Plug in 12 for x in the equation and try solving for y:
[tex] x = 3y^2 [\tex]
[tex] 12 = 3y^2 [\tex]
Divide both sides by 3
[tex] \frac{12}{3} = \frac{3y^2}{3} [\tex]
[tex] 4 = y^2 [\tex]
Take the square root of both sides
[tex] \sqrt{4} = \sqrt{y^2} [\tex]
[tex] \sqrt{4} = y [\tex]
[tex] y = \sqrt{4} [\tex]
[tex] y = -2 or 2 [\tex]
As you can see, there are two values of y (2, -2) for an x-value (12).
This does not represent a function.
Given equation [tex]x=3y^{2}[/tex] is not function.
Thus, option (4) is correct.
A function is a relation in which each possible input value leads to exactly one output value.
The output is a function of the input and The input values make up the domain, and the output values make up the range.
In equation x=y-2 , each possible input value leads to exactly one output value. So, this is function.
In equation [tex]y=3x^{2}[/tex], each possible input value leads to exactly one output value. So, this is function.
In equation y=2x+3, each possible input value leads to exactly one output value. So, this is function.
In equation, [tex]x=3y^{2}[/tex],
substitute x = 1
We get, [tex]1=3y^{2} \\\\y=\pm\frac{1}{\sqrt{3} }[/tex]
So, for single input value we get two value of output.
Therefore, equation [tex]x=3y^{2}[/tex]is not function.
Learn more about function here :
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