y=1/x-3 - 4
state the domain and range,
at first I though domain would be R (any real number) and range would be R also?
I'm not sure
Domain is X and range is Y. From the equation you can find the y and x.
To determine the domain and range of the function y = 1/(x-3) - 4, we need to consider any restrictions on the values of x and determine the set of possible values for y.
For the domain, we look for any values for x that would make the function undefined. In this case, the function has a denominator of (x-3), so we need to find the values of x that would make (x-3) equal to zero (since division by zero is undefined).
Solving (x-3) = 0, we find that x = 3. Therefore, the function is undefined at x = 3. Hence, the domain of the function is all real numbers except x = 3. In set notation, we can write the domain as D = R - {3}, where R means the set of all real numbers and {-} denotes the exclusion of 3.
For the range, we consider the function values of y. Since the function involves division and subtraction, it can take any value for y except when the function becomes undefined. As x approaches 3 from the left, the function approaches negative infinity, and as x approaches 3 from the right, the function approaches positive infinity. Therefore, the range of the function is all real numbers except negative infinity and positive infinity. In set notation, we can write the range as R = (-∞, ∞) - {-∞, ∞}.
To summarize:
Domain: D = R - {3}
Range: R = (-∞, ∞) - {-∞, ∞}