Interval Notation, Exponents and Radicals

Interval Notation When given a time period or interval of values, we often use inequality notation to describe the portion of the graph in which we are interested. In calculus, inequality notation is rarely used. More often we use interval notation to describe the portion of the graph.

Brackets vs. Parenthesis When using interval notation the smaller number always comes first. If we want to include the number (greater than or equal to) we use a bracket. If we do not want to include the number (greater than ___), we use parenthesis.

Examples Write in interval notation.

Unbounded Intervals Write in interval notation.

Laws of Exponents 1)When _________ bases, ______ exponents. 2)When _________ bases, _______ exponents.

3)When a monomial with different bases is raised to a power, the exponent must be applied to ______ bases. 4)When a power is raised to another power, ___________ the exponents.

Powers that are negative or zero Any base that is raised to the power of zero = ____. To make a negative exponent become positive, ______ _____ base and change the sign of the exponent.

“Common Sense” Rules 1)If, then __________. 2)If, then __________.

Exponents Examples 1)Simplify 2) Simplify

Properties of Radicals We cannot add or subtract radicals if the radicand is not the same.

Examples Simplify Write as a rational exponent

Rationalizing Radicals 1)Simplify 2)Rationalize the numerator

Homework Pg. 10 (19 – 27 odd, 31 – 35 odd) Pg. 23 (15 – 23 odd, 35 – 43 odd, 49 – 53odd, 61 – 67 odd, 73, 75)