Answer:
The range of the given absolute function is:
f(x)≤1
Step-by-step explanation:
We know that the range of a function is the possible values that is attained by the function i.e. the dependent variable in it's valid domain.
Clearly after looking at the graph we observe that the function attains all the values which are less than or equal to 1.
Since, the maximum value of the function is 1.
Hence, the range of the absolute value function below is:
f(x)≤1
The range of Absolute valued function is f(x)≤1.
The domain and range of a function are the components of a function. The domain is the set of all the input values of a function and range is the possible output given by the function. Domain→ Function →Range.
The range of a function is the set of all its outputs. Example: Let us consider the function f: A→ B, where f(x) = 2x and each of A and B = {set of natural numbers}.
Here we say A is the domain and B is the co-domain.
Then the output of this function becomes the range.
The range = {set of even natural numbers}.
The function y=|ax+b| is defined for all real numbers. So, the domain of the absolute value function is the set of all real numbers. The absolute value of a number always results in a non-negative value. Thus, the range of an absolute value function of the form y= |ax+b| is y ∈ R | y ≥ 0. The domain and range of an absolute value function are given as follows
Example: |6-x|
Domain: The domain of the function is the set R.
Range: We already know that the absolute value function results in a non-negative value always. i.e., |6-x| ≥ 0, for all x.
We know, that the range of a function is the all the possible values that is contained in a function.
By graph we can see that the function have value less than 1.
So, maximum value of function is 1
Hence, the range of the absolute value function is f(x)≤1.
Learn more about this range here:
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