Question

Consider the function represented by the equation y minus 6 x minus 9 = 0. Which answer shows the equation written in function notation with x as the independent variable?

Answer 1

f(x) = 6x + 9

Explanation:

The question is not complete because the are no option to pick from. This is the complete question.

Consider the function represented by the equation y minus 6 x minus 9 = 0. Which answer shows the equation written in function notation with x as the independent variable?

f of x = 6 x + 9

f of x = one-sixth x + three-halves

f of y = 6 y + 9

f of y = one-sixth y + three-halves

writing this in as a function

`f(x)-6x-9=0`

the question is asking us to write the function in such a way that x is the independent variable

`f(x)=6x-9`

here x is the dependent variable

to make x independent, we need to solve for x

`-9=6x\\`

divide both sides by 6 to make x independent

`(-9)/(6) =x\\\\\\\x=(-3)/(2)`

Answer 2

`f(x)=6x+9`

Explanation:

Functions have independet variables(the value of the variable could be any number, we have no restrictions) and dependent variaariables(the values of this variables depends of idependent variables)

the problem says that x is the independent variable, so we say that y is a dependent variable. Dependent need to be replaced by funcion notation, in this case we use y=f(x)

So we raplace it in the equation and we have:

`f(x)-6x-9=0`

we solve for f(x) passing -6x and -9 to the right side and changing the signs, and we get:

`f(x)=6x+9`