Question

Consider the function represented by the equation y-6x-9=0. Which answer shows the equation written in function notation with x as the independent variable? A.f(x)= 6x+9 B. f(x)=1/6x+3/2 C. f(y)=1/6y+3/2

Answer 1

There are two kind of variables when equation of a function is written

1. Independent variable

2. Dependent Variable

A variable is said to be independent , if it can select constant values by itself.

And, a variable is said to be independent, if it is dependent on other variable of the equation.

The given equation is , y-6 x -9=0

As, we have to write a function in which x is an independent variable and other variable y, will work as a dependent variable.

So, writing the above linear function as,

y= 6 x + 9

f(x)= 6 x + 9 →→Option (A)

Correct representation of function in which x is an independent variable and y is a dependent variable,because if we substitute different real values of x, we get different real values of y.

Answer 2

we have

`y-6x-9=0`

Step
`1`

Clear the variable y

`y-6x-9=0`

Adds
`(6x+9)` both sides

`y-6x-9+(6x+9)=0+(6x+9)`

`y=(6x+9)`

Step
`2`

Convert in function notation

Let

`f(x)=y`

`f(x)=(6x+9)`

therefore

the answer is

`f(x)=(6x+9)`