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Unit 1: Function Families

Unit 1: Function Families. Conditional Statements Vocabulary. What is a statement?. A statement is a sentence that is either true or false, but not both. Example: The Atlanta Thrashers are a pro basketball team. Non example: What’s your favorite music video?. What is a conjecture?.

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Unit 1: Function Families

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  1. Unit 1: Function Families Conditional Statements Vocabulary

  2. What is a statement? • A statement is a sentence that is either true or false, but not both. • Example: The Atlanta Thrashers are a pro basketball team. • Non example: What’s your favorite music video?

  3. What is a conjecture? • A conjecture is an unproven statement that is based on observations.

  4. What is a counterexample of a statement? • A counterexample is a specific case for which a conjecture is false.

  5. What is a conditional statement? • A conditional statement is a logical statement that has two parts, a hypothesis and a conclusion.

  6. What is “if-then” form? • The form of a conditional statement that uses the words “if” and “then.” The “if” part contains the hypothesis and the “then” part contains the conclusion.

  7. How do you negate a statement? • The negation of a statement is the opposite of the original statement.

  8. What is the converse of a statement? • The converse of a conditional statement switches the hypothesis and the conclusion.

  9. What is the inverse of a statement? • The inverse of a conditional statement negates the hypothesis and the conclusion.

  10. What is the contrapositive of a statement? • The contrapositive of a conditional statement: • First write the converse of the statement • Then negate both the hypothesis and the conclusion

  11. What is a biconditional statement? • A statement that contains the phrase “if and only if.” • When a statement and its converse are both true, you can write them as a single biconditional statement.

  12. Write the following statement in “if-then” form. • An angle is an acute angle if its measure is less than 90 degrees.

  13. “If-then” form • If the measure of an angle is less than 90 degrees, then it is an acute angle.

  14. What is the hypothesis and conclusion of the statement:If the measure of an angle is less than 90 degrees, then it is an acute angle.

  15. Write the inverse of the statement: If the measure of an angle is less than 90 degrees, then it is an acute angle.

  16. The inverse of the statement is: If the measure of an angle is not less than 90 degrees, then it is not an acute angle.

  17. Write the converse of the statement: If the measure of an angle is less than 90 degrees, then it is an acute angle.

  18. The converse of the statement is: If the angle is acute, then the measure of the angle is less than 90 degrees.

  19. Write the contrapositive of the statement: If the measure of an angle is less than 90 degrees, then it is an acute angle.

  20. The contrapositive of the statement is: If the angle is not acute, then the measure of the angle is not less than 90 degrees.

  21. Your Turn • Get with a partner. • Come up with two conditional statements; one related to mathematics and the other with real-world context. (They may be in “if-then” form or some other form.) • When you have come up with these two statements, raise your hand for me to check and take up your statements.

  22. Homework • Pick another classmates paper and complete the following types of statements for the math and real-world statements: • Write the converse • Write the inverse • Write the contrapositive

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