Domain and Range of Rational Functions - Varsity Tutors.
Start studying Domain and Range (inequality notation), Domain and Range - mixed practice, Domain and Range. Learn vocabulary, terms, and more with flashcards, games, and other study tools.
A real number is just an ordinary number. The set of real numbers include all numbers between negative and positive infinity. Real numbers are ordered, and thus do not include imaginary numbers.
Using interval notation we will show the set of number that includes all real numbers except 5. First, stated as inequalities this group looks like this: The statement using the inequalities above joined by the word or means that x is a number in the set we just described, and that you will find that number somewhere less than 5 or somewhere greater than 5 on the number line.
So -1 cannot be in the domain, because we cannot divide by 0. Thus, the answer is C: all real numbers except for -1. The general procedure to finding domain of a rational function is to set the DENOMINATOR equal to ZERO. Since we know that division by zero is not allowed, this will tell us the values at which the function is not defined.
If the index is an odd number, such as a cube root or fifth root, then the domain of the function is all real numbers, which means you can skip steps 2 and 3 and go right to step 4. If the index is an even number, such as a square root or fourth root, then to find the domain the expression inside the radical must be greater than or equal to zero.
The domain of a quadratic function in standard form is always all real numbers, meaning you can substitute any real number for x. The range of a function is the set of all real values of y that you can get by plugging real numbers into x.
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