Radicals and Rationals

Graphing Radical Functions & Solving Rational Exponents

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The above function is a radical function. The coefficient, a, is what changes the function's orientation and shape. If a is less than zero, the graph will be reflected across the x-axis. If |a| is greater than one, the graph is stretched vertically. If |a| is more than zero but less than one, the graph is compressed vertically.


The value h causes the horizontal translation of the function. The function would move h units right if h is positive, and left if it is negative.


The value k causes the vertical translation of the function. It will move k units up if it is positive, and k units down if k is negative.

Rational Exponents

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Rational, or fractional exponents can also be written in root form. Any number to the 1/2 power is the same as the square root of that number. In the practice problem done above, the eighth root of 81 is rewritten as 81 to the 1/8 power. Then, because 3 to the 4 is 81, it is written that way because there is also a 3 in the denominator. Then, the numerator is divided by the denominator, and exponents are subtracted. This leaves you with 3 to the 1/3 power, which is also the cubed root of 3.

The Two Concepts Come Together

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In this problem, both sides are multiplied by a power of 4 to eliminate the 1/4 power on the left side of the equation, or the quartic root of 6q+1. Then, the problem is solved.

The Basics of Rational Exponents and Radical Equations

Radical Equations & Rational Exponents

Upcoming quizzes/tests

Monday, December 9th- Quiz