# Radicals and Rationals

### Graphing Radical Functions & Solving Rational Exponents

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.

## Parent Radical/ Square Root Function The step pattern for the parent function is 1 right, 1 up from the vertex. The next point is 4 right, 2 up from the vertex. | ## Different Coefficient, h, and k The vertex of this function is moved 4 units right and 2 units up because of the h and k values. The a value, 3, causes the graph to be vertically stretched, as the coefficient is more than 1. This causes the step pattern to change, and the y value is multiplied by 3 when an x value is put in. Instead of going 1 over ad 1 up, it goes 1 over and 3 units up. | ## Step Pattern This shows the step pattern of the function. |

## Parent Radical/ Square Root Function

## Different Coefficient, h, and k

## Rational Exponents

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.