y = x This is a line and a function. Function values are y values.
Without the actual function we cannot help you very much.
The domain of a function encompasses all of the possible inputs of that function. On a Cartesian graph, this would be the x axis. For example, the function y = 2x has a domain of all values of x. The function y = x/2x has a domain of all values except zero, because 2 times zero is zero, which makes the function unsolvable.
"Domain" means for what numbers the function is defined (the "input" to the function). For example, "x + 3" is defined for any value of "x", whereas "square root of x" is defined for non-negative "x". "Range" refers to the corresponding values calculated by the function - the "output" of the function. If you write a function as y = (some function of x), for example y = square root of x, then the domain is all possible values that "x" can have, whereas the range is all the possible values that "y" can have.
All y-values in the function are multiplied by -1. This function is 'flipped' over the x-axis.
Suppose a function takes values of a variable, X, as its input, and that it converts it into an output value Y.Then the graph of the function, in the X-Y coordinate plane, is the set of all points (x, y) such that when you input the value x into the function, the output is y.Suppose a function takes values of a variable, X, as its input, and that it converts it into an output value Y.Then the graph of the function, in the X-Y coordinate plane, is the set of all points (x, y) such that when you input the value x into the function, the output is y.Suppose a function takes values of a variable, X, as its input, and that it converts it into an output value Y.Then the graph of the function, in the X-Y coordinate plane, is the set of all points (x, y) such that when you input the value x into the function, the output is y.Suppose a function takes values of a variable, X, as its input, and that it converts it into an output value Y.Then the graph of the function, in the X-Y coordinate plane, is the set of all points (x, y) such that when you input the value x into the function, the output is y.
If the function of the variable x, is f(x) then the roots are all the values of x (in the relevant domain) for which f(x) = 0.
The domain of the function means, for what values of the independent variable (input value) (or variables) is the function defined. If you have an equation of the type:y = f(x) ("y" somehow depends on "x") then the domain is all the values that "x" can take.
Yes, if the function is f(x) = 0 for all values of "x". Otherwise, it can't, since by definition, a function can only have one value for any "x".
Looking at the graph of the function can give you a good idea. However, to actually prove that it is even or odd may be more complicated. Using the definition of "even" and "odd", for an even function, you have to prove that f(x) = f(-x) for all values of "x"; and for an odd function, you have to prove that f(x) = -f(-x) for all values of "x".
These are usually the domain of the function.
They can be any values in the domain of the function.