Can somebody help me wit this?
Find the range and the domain of:
f(x)=(1/2)|x-2|
The domain is all real numbers (x) from -infinity to infinity
The range (of f(x)) is 0 to infinity, since it can never be negative. f(x) has a minimum value of zero when x=2.
To find the domain of a function, you need to determine the set of all possible values for the independent variable (in this case, x) that will result in a real output for the function.
In the given function, f(x) = (1/2)|x-2|, there are no restrictions or limitations on the value of x. Since absolute value can be applied to any real number, there are no values of x that would make the function undefined. Therefore, the domain of f(x) is all real numbers, from negative infinity to positive infinity.
To find the range of a function, you need to determine the set of all possible values for the dependent variable (in this case, f(x)) that the function can take on.
In the given function, f(x) = (1/2)|x-2|, the absolute value of any number is always non-negative. The expression (1/2)|x-2| takes the absolute value of (x-2) and then scales it down by a factor of 1/2. This means that the minimum value the function can take is 0, which occurs when (x-2) is equal to 0. So, the function has a minimum value of 0 when x = 2.
Since the absolute value of any number is always non-negative, the function will only output values that are greater than or equal to 0. Therefore, the range of f(x) is from 0 to positive infinity. It can never be negative.