Find the domain of the relation then draw the graph.
A function must have a value for any given domain. For each edge (or interval), the sign graph has a sign (+ or -) . So, it is a function.
all real numbers
The domain of a function is the set of it's possible x values that will make the function work and output y values. In this case, it would be all the real numbers.
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 domain could be the real numbers, in which case, the range would be the non-negative real numbers.
Domain of the logarithm function is the positive real numbers. Domain of exponential function is the real numbers.
The domain of the sine function is all real numbers, or (-∞, ∞). Note the curly brackets around this interval, when a domain or range includes positive or negative infinity, it is never inclusive.
The domain of the sine function is all real numbers.
It is infinite, in both directions. But it can be restricted to a smaller interval.
The domain of your function is the set of real numbers.
The domain of a function is the set of numbers that can be valid inputs into the function. Expressed another way, it is the set of numbers along the x-axis that have a corresponding solution on the y axis.
One of them can be whatever you like: integers, rational numbers, real numbers, complex numbers, any of the previously mentioned within some interval. And then the other is determined.
A function must have a value for any given domain. For each edge (or interval), the sign graph has a sign (+ or -) . So, it is a function.
all real numbers
the domain of the function
To an extent, the answer depends on what the range is. The domain can be the set of complex numbers, with the range also the complex numbers. The domain can be the whole of the real numbers if the range can be complex. If the range needs to be real, then the domain must be the real numbers excluding the interval (0,9). As the range is restricted (rational, integer), the domain will also shrink.
The cotangent function has domain all real numbers except integral multiples of pi./2(90degrees).