More on Functions
Your homework from this lesson is not in the book, it is posted here.
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Problems 1-21 ask you to find the domain of a function. You can answer these problems by starting with the set of all real numbers as your domain, then excluding numbers that make the denominator zero or make the number underneath an even root sign negative. Since there are no radicals in problems 1-9, all you have to do is set the denominator equal to zero and solve for x. Your domain will then be all real numbers except the ones that made the denominator zero. Problems 2-5 lead to quadratic equations, which are reviewed here or view Movie 6.31 on this page. You must have QuickTime Player, a free download, installed on your computer. Problems 8-9 lead to equations with absolute values, which are reviewed here or you may view movie 2.24 on this page. For help on problem 10, you may view movie 4.14 on this page. Problems 12, 14, 16, and 17 lead to quadratic inequalities, which are reviewed in movie 6.34 on this page.
Problems 20-25 ask you to find the x-intercepts. This is done by setting the right side of the equation equal to zero and solving for x. Problem 23 leads to a radical equation which you can solve by first isolating the radical on one side of the equation, then raising both sides of the equation to the fourth power. Problems 24-25 lead to equations with rational exponents, which are reviewed in movie 7.14 on this page.
Problems 13 and 26 lead to rational inequalities, which are reviewed here.
Problems 27-30 result in inequalities with absolute value, which are reviewed here.