Skill7 undefined expressions
- 1. Skill 7 Undefined Expressions page 68 and 69 in the book NO Calculator allowed. There are two times in mathematics that problems can be undefined. These are: • Having a zero in the denominator of a fraction • Having a negative inside a square root There is nothing to do with this one. It is undefined because of the 0 in the bottom of the fraction. This could be a test question. The answer would be 2 because that number would make the denominator 0.
- 2. The only part of the problem you pay attention to is the bottom of the fraction. There are two multipliers (x) and (x + 1). Take them one at a time. Think about what value makes each a zero. The x is easy. What makes it a 0 is 0. That is one of the answers. Now look at (x + 1). What makes that 0? If x were -1, you would have -1 + 1 which is 0 so, -1 is another answer. So, the two values that make this undefined are 0 and -1.
- 3. Look at the two multipliers on the bottom. Take them one at a time. What makes (x + 2) equal 0? That would be -2. So, that is one answer. What makes (x – 5) equal 0? That would be 5. So, that is another answer. The two values that make this undefined are -2 and 5. End of problem!
- 4. Now, look at problems involving square roots? √x is the best way in PowerPoint I can write the square root of x. What makes this undefined? Well, if you had to choose from a list of answers, it would be any negative number. So, if your choices are a. 1 b. -2 c. 3 d. 0 It would be b. -2 That is too easy for the test! Sometimes, you have to do some algebra to tell if the number under the square root sign is negative. Because you don’t have access to a calculator, you have to be careful with the integers. Simplify each part to see which one is negative. Answer is B because (-2)(-2)(-2) is -8. All the others are positive and defined.
- 5. In this problem, you have to substitute the number supplied by the problem. Here The problem writer picked a value of -4 for y. Replace y with -4 in all the expressions and see which one gives a negative value. It is D because 2 (-4) is -8. This would mean the value under the square root sign is negative. That makes it undefined. All the other problems give a positive when y is replaced with -4.