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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