By definition, it is the set of all real numbers!
The absolute value of a number is positive, so the range is always a positive real number. You are correct. The domain, that is the value before you take the absolute value, is all real numbers, but the range is always positive.
(2x+3) / 5 Domain = All Real Numbers Range = All Real Numbers
It could be a subset: for example, for the function y = log(x), the domain is x > 0. There are many functions whose domain is the complex plane.
The domain of y = -4x is all real numbers.
the domain is all real numbers and the range is all real numbers the domain is all real numbers and the range is all real numbers
The range of y = nx consists of all positive real numbers, and the domain consists of all real numbers.
No. The domain is usually the set of Real numbers whereas the range is a subset comprising Real numbers which are either all greater than or equal to a minimum value (or LE a maximum value).
y = 1/x
Some functions are only defined for certain values of the argument. For example, the the logarithm is defined for positive values. The inverse function is defined for all non-zero numbers. Sometimes the range determines the domain. If you are restricted to the real numbers, then the domain of the square root function must be the non-negative real numbers. In this way, there are definitional domains and ranges. You can then chose any subset of the definitional domain to be your domain, and the images of all the values in the domain will be the range.
The domains of polynomial, cosine, sine and exponential functions all contain the entire real number line. The domain of a rational function does not, since its denominator has zeros, and neither does the domain of a tangent function. (1/2)x = true (8/3)x = true
By definition, it is the set of all real numbers!
The domain is all real numbers, and the range is nonnegative real numbers (y ≥ 0).
The absolute value of a number is positive, so the range is always a positive real number. You are correct. The domain, that is the value before you take the absolute value, is all real numbers, but the range is always positive.
(2x+3) / 5 Domain = All Real Numbers Range = All Real Numbers
The domain of the sine function is all real numbers.
The domain of cosine is all real numbers, its range is [-1,1], and its period is 2π radians.