- #1
KOO
- 19
- 0
What is the image of the function f: R -> R, f(x) = (x-2)^4
I think [0,∞)
Am I right?
I think [0,∞)
Am I right?
A function is a mathematical concept that relates each input value (x) to a unique output value (f(x)). In this case, the function f(x) = (x-2)^4 takes any real number as an input and returns a real number as an output.
The notation "f: R->R" indicates that the function f maps real numbers (denoted by R) to real numbers. In other words, both the input and output values of this function are real numbers.
To graph the function f(x) = (x-2)^4, you can plot a few points by choosing different values for x and calculating the corresponding values of f(x). Then, connect these points with a smooth curve to get the graph of the function.
The domain of a function is the set of all possible input values. In this case, the function f(x) = (x-2)^4 has a domain of all real numbers since any real number can be plugged in for x. The range of a function is the set of all possible output values. For this function, the range is all non-negative real numbers since raising a real number to the fourth power always results in a non-negative value.
The number "2" is known as the constant term in this function. It determines the vertical shift or translation of the graph of the function. In this case, the graph will be shifted 2 units to the right in comparison to the graph of the basic function f(x) = x^4.