How to find the domain and range of the function. -2Sgn(4x+8)-1 Write an equivalent equation.
To find the domain and range of a function, we need to examine the restrictions on the input values (domain) and the output values (range).
1. Domain: The domain of a function consists of all possible input values (usually denoted by x) for which the function is defined. To find the domain, we need to consider any restrictions on the input values, such as avoiding division by zero or taking the square root of a negative number.
In the given equation, we have -2Sgn(4x+8)-1. Since the sign function (Sgn) is defined for all real numbers, there are no restrictions on the input value (4x+8). Therefore, the domain of this function is all real numbers.
2. Range: The range of a function represents all the possible output values (usually denoted by y) that the function can attain. To determine the range, we need to analyze how the function behaves as the input values change.
In this case, the function -2Sgn(4x+8)-1 multiplies the sign function (-1, 0, or 1) by -2 and subtracts 1. The product of -2 times the sign function will always result in -2, 0, or 2. After subtracting 1, the function can have the output values -3, -1, or 1. Hence, the range of this function is {-3, -1, 1}.
Equivalent equation:
The given equation, -2Sgn(4x+8)-1, does not have an equivalent equation in the form of a single equation due to the nature of the sign function. However, you can rewrite the equation as follows:
y = -2Sgn(4x+8)-1
This way, you have an equivalent equation that relates the output value (y) to the input value (x) using the sign function.