1 / 12

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.

espriggs
Télécharger la présentation

Radical functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related