Bell ringer 1-27-17 1. Explain the difference between the vertical line test and the horizontal line test. 2. When will you need to restrict the domain of a function? Give an example of a function that requires a restriction. 3. Which Parent Functions on the poster beside the TV have inverse functions without restricting the domain? (Remember the cubic picture isn’t perfect.)

Finding the inverse algebraically Friday, January 27, 2017

Week of Inspirational math day 4 Speed is Not Important

What is the rule??? 20 – 10 – 5 – 16 – 8 – 4 – 2 – 1

Hailstone Sequences follow these rules: If a number is even, divide it by 2. If a number is odd, multiply it by 3 and add 1. Hailstones go up and down… They start in a cloud as drops of rainwater, then they are pushed higher in the atmosphere where they freeze, sometimes several times, before eventually falling back to earth.

http://tutorial.math.lamar.edu/Classes/Alg/InverseFunctions.aspx

http://tutorial.math.lamar.edu/Classes/Alg/InverseFunctions.aspx

http://tutorial.math.lamar.edu/Classes/Alg/InverseFunctions.aspx

Here’s the graph of the function and its inverse Here’s the graph of the function and its inverse. You can check by graphing to see that the function and its inverse are reflected over the line y = x. http://tutorial.math.lamar.edu/Classes/Alg/InverseFunctions.aspx

http://tutorial.math.lamar.edu/Classes/Alg/InverseFunctions.aspx

http://tutorial.math.lamar.edu/Classes/Alg/InverseFunctions.aspx

Here’s the graph of the function and its inverse Here’s the graph of the function and its inverse. You can check by graphing to see that the function and its inverse are reflected over the line y = x. http://tutorial.math.lamar.edu/Classes/Alg/InverseFunctions.aspx

http://tutorial.math.lamar.edu/Classes/Alg/InverseFunctions.aspx

http://tutorial.math.lamar.edu/Classes/Alg/InverseFunctions.aspx

Classwork 1. f(x) = -5x 6. f(x) = 𝑥 −1 𝑥+5 2. f(x) = 2x – 3 Find the domain and range of each function. Then, find the inverse algebraically, restricting the domain if necessary. 1. f(x) = -5x 6. f(x) = 𝑥 −1 𝑥+5 2. f(x) = 2x – 3 7. f(x) = 4 −𝑥2 3. f(x) = 3x + 10 8. f(x) = |x – 2| 4. f(x) = 4x – 3 9. f(x) = -2x2 + 5 f(x) = 4 𝑥 10. f(x) = x2 – 2x + 1

homework 1. f(x) = 15x – 1 2. f(x) = 1 3 x + 7 3. f(x) = -5x – 11 Find the domain and range of each function. Then, find the inverse algebraically, restricting the domain if necessary. 1. f(x) = 15x – 1 2. f(x) = 1 3 x + 7 3. f(x) = -5x – 11 4. f(x) = (x – 2)2 5. f(x) = 𝑥−4

Exit ticket Explain the process of finding the inverse of a function algebraically.