Question

Consider the function represented by 9x+3y=12 with x as the independent variable. How can this function be written using function notation?

a) f(y)=−3x+4
b) f(x)=−3x+4
c) f(x)=−4x+3
d) f(y)=−3y+4

Answer 1

To write 9x+3y=12 using function notation, solve for y in terms of x which gives y = 4 - 3x. Then express it as f(x) = 4 - 3x. The correct answer from the options provided is b) f(x) = -3x + 4.

Step-by-step explanation:

To write the function 9x+3y=12 with x as the independent variable using function notation, we need to solve for y in terms of x. We can do this by first isolating y on one side:

• 9x + 3y = 12
• 3y = 12 - 9x
• y = 4 - 3x

Now, we can express this using function notation, where f(x) represents our function in terms of x:

f(x) = 4 - 3x

From the options given, the correct expression using function notation for the function represented by 9x+3y=12 is f(x) = 4 - 3x, which corresponds to option b) f(x) = -3x + 4.