consider the function represented by with x as the independent variable. how can this function be written using function notation?
You’re asking a very standard algebra question, but the exact function is missing from your text. It sounds like it originally came from a worksheet or screenshot such as:
“Consider the function represented by ______ with x as the independent variable. How can this function be written using function notation?”
Since I can’t see the actual expression, I’ll show you the pattern so you can plug yours in.
Key idea: function notation
When a relationship is written with xxx as the independent variable and yyy as the dependent variable, it usually starts as an equation like:
- y=(some expression in x)y=\text{(some expression in }x\text{)}y=(some expression in x)
To write this using function notation, you:
- Choose a function name, most commonly fff.
- Replace yyy with f(x)f(x)f(x).
So:
- If you have y=3x+2y=3x+2y=3x+2, the function notation is f(x)=3x+2f(x)=3x+2f(x)=3x+2.
- If you have y=11+x2y=\dfrac{1}{1+x^2}y=1+x21, the function notation is f(x)=11+x2f(x)=\dfrac{1}{1+x^2}f(x)=1+x21.
- If you solve an equation like x−y=3x-y=3x−y=3 for yyy, you get y=x−3y=x-3y=x−3, so in function notation it becomes f(x)=x−3f(x)=x-3f(x)=x−3.
How to convert yours
Do this with your specific problem:
- Isolate yyy (if needed):
- Rearrange the given equation so it looks like y=(expression in x)y=\text{(expression in }x\text{)}y=(expression in x).
- Replace yyy with f(x)f(x)f(x):
- Once you have y=expression in xy=\text{expression in }xy=expression in x, write
f(x)=expression in xf(x)=\text{expression in }xf(x)=expression in x
That final f(x)=…f(x)=\dots f(x)=… is “the function written in function notation with xxx as the independent variable.”
If you paste the exact equation
If you can send the specific function (for example, “9x – 3y = 12” or “x – y = 3”), I can write the exact function-notation form step by step for that exact expression.