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

y-6x -9 =0

add 6x+9 to both sides

y=6x+9

It's graphically a line with slope 6 and y intercept +9

Answer 2

Dear Natalia,

Function notation means that your answer is going to be in the format: f(x) =

Of course, you can use g(x), h(x), r(x), or whatever you want. I will use f(x).

x is what goes into the function; f(x) is what comes out of the function. x is called the independent variable, because you pick it and f(x) is locked in or DEPENDENT on your choice of x.

y is equivalent to f(x) in this case. Kind of confusing, I know.

Let's first translate the first English sentence of the problem into mathematical language.

Consider the function represented by the equation y minus 6 x minus 9 = 0.

y – 6x – 9 = 0

Now, let's get the y by itself on one side of the equation.

y – 6x – 9 + 9 = 0 + 9

y – 6x = 9

y – 6x + 6x = 9 + 6x

y = 9 + 6x

y = 6x + 9

Now we simply substitute f(x) for y to get:

f(x) = 6x + 9

And that's your answer!!!

Answer 3

y - 6x - 9 = 0 → solving for "y"

y = f(x) = 6x + 9 → function "y" is a written in a function notation with "x" as the independent variable