What is the independent variable?

Question

f(x)=5x^3-7x^2+2x-1

The question asks
"state the independent variable and the domain."

Could someone help refresh my memory on how to find these two things because I don't remember...thanks =)

So what would be the independent variable in this equation?

So...is the independent variable in a function always x?

Answer 1

The independent variable is the one you can change arbitrarily. For any function f(x), x is the independent variable. If you have y = f(x), then y is the dependent variable; its value depends on that of x. If you have z = f(x, y), x and y are both independent variables and z is dependent.

Note that although x is usually the indepent variable, it isn't always true. If you have x = f(y), then y is the independent variable and x is dependent.

The domain is the set of values for the independent variable for which the value of the function is defined. For any polynomial function, which f(x) is in this case, the domain is all real numbers.

Answer 2

1) write it as

y = 5x^3- 7x^2 +2x-1, and you see y is the DEPENDENT variable, because it depends on x, and x is the INDEPENDENT variable, because it is free to vary as you wish it to.

2) the domain is the set of allowable values for x, the independent variable.

Tip: for ANY polynomial, this set is R, or all real numbers.

Answer 3

Think of the notation f(?) as an input/output machine.
The ? is going to be input to this input/output machine (kind of like a meat grinder; that's the way I think of it...) The ? goes in and something comes out.
Whatever comes out is expressed as f(?). The f() notation tells you that some kind of grinding is going on with that meat. Whatever the notation f() means DEPENDS on what you put in the machine. That thing you put in it, whatever it is, is independent of the machine. You pull it from somewhere, stick it in the machine, grind it out and the result is your output.
Using the visual of a meat grinder, you put sirloin in and something comes out that is different from another 'independent' thing of the same type, like pork or mmmmmm, lamb.
The f(?) is an expression for that output.
f(x) is the output of the input x.
f(y) is the output of the input y.
f(n) is the output of the input n.
beef, pork, lamb, what does it matter? They are independent items that can be pulled in to the process (grinding).
f(x), f(y), f(n) are expressions of what happens when you have processed whatever input - in this case, x, y, n - for the functions f(). Are they the same function or different functions? You can see what the function actually is by checking out the other side of the equals sign. The other side of the equals sign tells you what the process is that's preparing that stuff, that meat.
What is the process? The stuff that you see on the other side of the equals sign. That expresses all that is being done to what you threw in that grinder... spices, herbs, maybe something got precooked too before it got mixed in!
So, for example: f(n) = 5n - 1
You can see that n is the independent variable.
5n-1 is all the culinary magic you performed on n if n were a meat.
f(n) = 5n -1 expresses equality. The f(n) which is an expression of output with n as it's input is equal, is the same as, 5n-1 which is the process of taking n and slapping it on a butcher block and pounding some cracked pepper (-1) into it.
What you have is n slapped on a butcher block and pounded with seasoning. It is exactly the same, because of the equals sign, to the expression f(n).
Confused?
Oh, well, it was fun bringing meat into math!
Oh, and domain? Those are all the acceptable items you can use with that machine. I wouldn't try to pound cracked pepper into a hunk of raw flounder so I guess flounder is not going to be included in the domain! Splat!

Answer 4

The independent variable in this equation is x.

The domain is the values the independent variable may take on. In this case, x may take on the values of the complex number field.

The dependent variable gets its value from the rule specifying the operations to be preformed on the independent variable.

Answer 5

An independent variable is a variable that is controlled or fixed by the researcher. This variable may have an effect on the dependent variable. Also known as X-variable, predictor variable, explanatory variable, and factor.

Answer 6

x is the independent variable

f(x)=5x^3-7x^2+2x-1 also y= 5x^3-7x^2+2x-1

domain are the x values and range is the y values

if x = 0 than y = -1
i believe if x =1 than y = -1

Answer 7

It is universally accepted that, graphically, x is the independent variable and f(x), or y, is the dependent variable. If not, the stock market would be a mess. What if the definitions of left & right were not universally accepted? Or, more importantly, right & wrong?

Answer 8

The golf ball depends on how much force you use. underline golf and box force. The amount of ink depends on how many weeks you use the pen. The total cost of taxable items depends on the amount the person pays in tax.

Answer 9

for the domain, you solve for x