Understanding Domain and Range: Definitions and Examples Master the concepts of domain and range in mathematics with comprehensive explanations and clear examples. Boost your understanding and skill in determining the domain and range of various functions.

How do you find domain and range of a function?Ex. f(x) = X^2Ex. f(x) = √(x+4) -2 Ex. f(x) = 3lxl + 4

To find the domain and range of a function, we need to understand the definitions of domain and range first

To find the domain and range of a function, we need to understand the definitions of domain and range first.

The domain of a function is the set of all possible input values (x-values) for which the function is defined. In other words, it is the set of values that can be plugged into the function.

The range of a function is the set of all possible output values (y-values) that the function can produce. In other words, it is the set of values that the function can take on.

Let’s find the domain and range for each function:

1. f(x) = x^2
In this case, the function is a simple quadratic function.
– The domain of this function is all real numbers because there are no restrictions on the input values.
– The range of this function is all non-negative real numbers since the square of any real number is non-negative.

Domain: (-∞, ∞)
Range: [0, ∞)

2. f(x) = √(x+4) – 2
This function is a square root function with a horizontal shift of 4 units to the left and a vertical shift of 2 units downward.
– The domain of this function is the set of all real numbers for which the expression inside the square root is non-negative. In this case, x + 4 ≥ 0, which means x ≥ -4.
– The range of this function is all real numbers greater than or equal to -2, since the vertical shift is downward by 2 units.

Domain: [-4, ∞)
Range: [-2, ∞)

3. f(x) = 3|x| + 4
This function involves an absolute value. The absolute value of a number is always non-negative.
– The domain of this function is all real numbers since the absolute value of any real number is always defined.
– The range of this function is all real numbers greater than or equal to 4, since the absolute value function will always yield a non-negative value.

Domain: (-∞, ∞)
Range: [4, ∞)

It is important to note that domain and range may vary depending on the specific type of function and any restrictions or transformations applied to it. It is always a good idea to carefully analyze the function to determine the appropriate domain and range.

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