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Warm Up

Warm Up. Find the inverses for the following functions: Use algebra to determine if the following functions are inverses of each other (no graphing, no tables)…. LOGARITHMS Pt. 1. Sec 6.2.1. Learning Targets. Finding the inverse of an exponential function

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Warm Up

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  1. Warm Up • Find the inverses for the following functions: • Use algebra to determine if the following functions are inverses of each other (no graphing, no tables)…

  2. LOGARITHMS Pt. 1 Sec 6.2.1

  3. Learning Targets • Finding the inverse of an exponential function • Investigating the Logarithmic Function • How to use the Logarithmic Function

  4. Known inverses: • Linear • Quadratic • Cubic • term • Absolute Value • Hyperbola WHATS MISSING?!? EXPONENTIAL FUNCTIONS

  5. Graph the Inverse of the Following Function • Use a table and the definition of an inverse…

  6. What do you notice about it… • List of Characteristics: • Asymptote of • Grows very slowly… • Opposite of our exponential!!! • We call this function a Logarithmic Function • It “undoes” an exponential function when the independent variable is the exponent

  7. Before we go too deep into the inverse lets understand Log(arithm) • P. 278: 6-56 • Mathematicians first created a puzzle in ancient India in the 2nd Century BCE. More recently, about 700 years ago, Muslim mathematicians created the first tables allowing them to find answers to this type of puzzle quickly. • Here are some clues to help you figure out how the puzzle works: • Use these clues to solve for a-f

  8. Log Notation • What do these clues tell us? • Log form is equivalent the exponential form Ex: EXPONENT BASE

  9. Practice • 6-68 Modified: Fill in the table. • Try looking at your table in the calculator!!! What base is this function?

  10. Practice • 6-68 Modified: Fill in the table.

  11. Notation • The base for is always going to be in base 10. • The only time this changes is when the base is stated. • How to use in calculator: MATH  logBASE Now you can find the outputs for any base!!!

  12. Practice • 6-68 Modified: Fill in the table.

  13. Log Values • What inputs are not valid for Logs? Why? • Pause and Ponder SILENTLY to come up with a reason… • Oh yea that’s right our exponential function will never give us negative output’s (asymptote)! Therefore we cannot have negative inputs for inverse! • Remember an inverse function “undoes” the original function • Original: XY Inverse:YX

  14. Back to Inverses of Log’s Find the inverse for: (Hint: write it in log form) You should have the function: Remember we switch the x and y…

  15. You try… • Do problem 6-70 a-d: •  •  •  •  • Remember to always check your answers….

  16. Lets solve the following…

  17. Your Inverse Toolkit • You should be able to go through your notes and find the following information: • Define what an inverse is and when a function will have one. • Find a functions inverse by “undoing” • Prove if two functions are inverses by using: • Table • Graph • Composition • Restrict the Domain for non-invertible functions in order to come up with an inverse • Use Log’s to solve and invert exponential functions that has an input unknown for the exponent

  18. On your own • Review your notes and seek help on subjects that are unclear or need reinforcing. • Please fill out an index card that answers the following: • During this unit the topic that is most unclear up to this point is? Why? • Homework • 6-69, 6-71, 6-73-6-77 • 6-87-6-91

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