Respuesta :

absor201

The range is: B. {12, 4, -6}

Step-by-step explanation:

Given

12x + 6y = 24

Here x is the input and y is the output

So,

Replacing y with f(x)

[tex]12x +6f(x) = 24\\6f(x) = 24 - 12x\\\frac{6f(x)}{6} = \frac{24-12x}{6}\\f(x) = \frac{24-12x}{6}[/tex]

Domain =  {-4, 0, 5},

We will put the elements of domain, one by one, to find range

[tex]f(-4) = \frac{24-12(-4)}{6}\\=\frac{24+48}{6}\\= \frac{72}{6}\\=12\\\\f(0) = \frac{24-12(0)}{6}\\=\frac{24}{6}\\= 4\\\\f(5) = \frac{24-12(5)}{6}\\=\frac{24-60}{6}\\=\frac{-36}{6}\\=-6[/tex]

Hence,

The range is: B. {12, 4, -6}

Keywords: Range, Domain, functions

Learn more about functions at:

  • brainly.com/question/3375830
  • brainly.com/question/3398261

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johngaming220

{12, 4, -6}

Step-by-step explanation:

The relation is given by the equation as 12x + 6y = 24 ........... (1)

Now, the domain of this function is {-4, 0, 5}

We have to find the range of this function corresponding to the given domain.

Now, for x = - 4,  

12(-4) + 6y = 24 {From equation (1)}

⇒ 6y = 72

⇒ y = 12

Now, for x = 0,  

12(0) + 6y = 24 {From equation (1)}

⇒ 6y = 24

⇒ y = 4  

Now, for x = 5,  

12(5) + 6y = 24 {From equation (1)}

⇒ 6y = -36

⇒ y = -6

Hence, the range for the relation is {12, 4, -6} (Answer)

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