Consider the function represented by 9x+3y= 12 with x as the independent variable. How can this function be written using
function notation?
O f(x) = - 2 / 3 x + 2/3
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f(x) = -3x + 4

Second option

Step-by-step explanation:

In function notation, the "y" variable is isolated and replaced with "f(x)".

Isolate "y" by keeping "y" on the left and moving everything else to the right. To move something, do its reverse operation to both sides.

9x + 3y = 12

9x + 3y - 9x = 12 - 9x                  Do -9x on both sides

3y = -9x + 12

3y/3 = -9x/3 + 12/3                      Divide by 3 on both sides

y = -3x + 4                             Change to function notation

f(x) = -3x + 4                         Answer

g(x) = x² + 2

step-by-step explanation:

it is given that the graphs are the same shape.

the only difference is that the red graph is 2 units higher than the blue graph.

that is to say that the red graph is simply the blue graph that has been moved vertically by 2 units in the positive y direction.

hence

g(x) = f(x) + 2

or

g(x) = x² + 2