What is meant by “the domain of a function is (−∞, ∞)”?
that means there is a y for every value of x between −∞ and +∞
for example that would not be true for
y = 7/ (x-1)
because there is no y when x = 1
just for future reference, this domain is good for
all polynomials
all exponentials
all sines and cosines
When it is said that "the domain of a function is (-∞, ∞)," it means that the function is defined for all possible real numbers. In other words, there are no restrictions on the values that can be input into the function. The domain, in this case, spans from negative infinity (−∞) to positive infinity (∞), indicating that the function is defined for any real number.
The statement "the domain of a function is (-∞, ∞)" means that the function is defined for all possible input values. In other words, the domain of the function includes all real numbers from negative infinity to positive infinity.
To understand this concept, it's helpful to visualize the number line. In the case of a function with a domain of (-∞, ∞), every single point on the number line is a valid input for the function. There are no restrictions or limitations on the type of input allowed.
For example, if you have a function f(x) = x^2, the domain would be (-∞, ∞) because you can plug in any real number for x and get a corresponding output. Whether you choose -100, 0, or 100 as an input, the function will always produce a valid output.
To determine the domain of a function, you should consider any restrictions or limitations that exist. However, if you see that the domain is (-∞, ∞), it means that there are no restrictions or limitations on the inputs, and the function is defined for all real numbers.