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Radical functions

Radical functions. Information. Radicals. A radical is the root of a number. radical sign. root index. n. √ a. radicand. When the radical sign is written without a root index it is a square root. The unwritten index is a 2.

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Radical functions

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  1. Radical functions

  2. Information

  3. Radicals A radical is the root of a number. radical sign root index n √a radicand When the radical sign is written without a root index it is a square root. The unwritten index is a 2. A number b is the squareroot of a number a if b2 = a. For example, 6 is the square root of 36 because 62 = 36. A number b is said to be the cuberoot of a number a if b3 = a. For example, 2 is the cube root of 8 because 23 = 8.

  4. Inverse operations How do you “undo” addition? subtraction 2+ 3 = 5 5– 3 = 2 Addition and subtraction are inverse operations. Adding a number and then subtracting the same number gives the number you started with. How do you “undo” multiplication? division 7× 4 = 28 28÷ 4 = 7 Multiplication and division are also inverse operations. How do you “undo” squaring a number? take the square root 25 = 5 52 = 25

  5. Square root

  6. Graphing other square root functions What do you think the graph of f (x) = x – 4 will look like? Complete the table of values for y = x – 4 and sketch its graph. Use the graph of y = x to help you. y x 0 –4 1 –3 4 –2 9 –1 16 0 y = x – 4 has the same shape as y = x, but has been translated vertically. 25 1

  7. Domain and range

  8. Pendulum clock A pendulum swings back and forth on a large clock. It takes 1.5 seconds to perform a complete oscillation. The time period of oscillation is modeled by the formula T = 2.006 L where L is the length of the pendulum in meters and T is measured in seconds. How long is the pendulum? How can you solve this using a graphing calculator?

  9. A graphical solution We are looking for the length, L, that corresponds to the time, T, of 1.5 seconds. In terms of the graph, we are given y and are looking for x. Look at the intersection of the graphs y = 2.006 x and y = 1.5 The pendulum is 0.56 meters long.

  10. Cube root

  11. Graphing other cube root functions What do you think the graph of f (x) = x + 3 will look like? Complete the table of values for y = x + 3 and sketch its graph. Use the graph of y = x to help you. x y -27 0 -8 1 -1 2 0 3 1 4 8 5 y = x + 3 has the same shape as y = x, but has been translated vertically. 27 6

  12. Translations

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