Limits (or limiting values) are values that a function may approach (but not actually reach) as the argument of the function approaches some given value. The function is usually not defined for that particular value of the argument.
"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.
No, it is not. Length is a metric that is defined as the absolute value of the distance between two points.
The number of function is Geometry
The unit step function at t=0 is defined to have a value of 1.
Trigonometric functions are defined from a numeric domain to a numeric range. So the input number determines whether or not the function is defined for that value and, if so, what the value of the function is.
Because that is the way the tan function is defined!
Absolutely. Indeed, any function (user-defined or built-in) that does not return a value is not really a function, it is simply a procedure.
Yes, if the function is equal to zero at x=0, the function is considered defined at that point. The function's value at x=0 does not impact its overall definition.
Limits (or limiting values) are values that a function may approach (but not actually reach) as the argument of the function approaches some given value. The function is usually not defined for that particular value of the argument.
"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.
Both the Greatest Integer Function and the Absolute Value Function are considered Piece-Wise Defined Functions. This implies that the function was put together using parts from other functions.
No, it is not. Length is a metric that is defined as the absolute value of the distance between two points.
The number of function is Geometry
The "zero" or "root" of such a function - or of any other function - is the answer to the question: "What value must the variable 'x' have, to let the function have a value of zero?" Or any other variable, depending how the function is defined.
The unit step function at t=0 is defined to have a value of 1.
f(x) = 2 cos 3x The amplitude: A = |2| = 2 The maximum value of the function: 2 The minimum value of the function: -2 The range: [-2, 2]