1 / 21

Bell work

Bell work. Find the value to make the sentence true. NO CALCULATOR!! 2 3 = x 5 x = 25 (½) 3 =x X (1/2) = 5. Graph f(x) = 2 x Name 3 points on f(x) Graph y = x Graph f -1 (x) Write an equation for the inverse.

lamar-bruce
Download Presentation

Bell work

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. Bell work Find the value to make the sentence true. NO CALCULATOR!! • 23 = x • 5x = 25 • (½)3=x • X (1/2) = 5

  2. Graph f(x) = 2x • Name 3 points on f(x) • Graph y = x • Graph f-1 (x) • Write an equation for the inverse.

  3. F(x) = 2xto write the equation of the inverse, switch the x and y values x = 2y How do you solve for y? Verbally we would say that “Y is the exponent that 2 to raised to in order to get x.” To write it mathematically: y = log2x

  4. A logarithm is just an exponent • So the inverse of an exponential function is a logarithmic function. (This means that exponentiation “undoes” logarizing and vice versa.) Definition of logarithm: X = ay can be rewritten as logax = y (a>0, a≠1, x>0) ** Why is domain positive? ** What # can be raised to power and give you a negative? **

  5. Any exponential expression can be written as a logarithmic expression and vice versa Rewrite in exponential form. • log28 = 3 • log381=4 • log164 = ½ • log273 = ⅓

  6. Any exponential expression can be written as a logarithmic expression and vice versa Rewrite as a logarithmic expression. • 52 = 25 • 34 = 81 • (½)3 = ⅛ • (2)-2 = ¼

  7. Remember: A logarithm is an exponent Evaluate. • log216= ** Think: 2 to what power gives me 16?** • log327= _____ • log22=_____ • log101000=____ • 2 log31= _____

  8. Common logarithm • The common logarithm is a log with base of 10. • When the base is 10, we don’t write it!! • Example: log 100 = 2 (Understood base 10) • The calculator uses the common base of 10 when you plug in a value. • Use the calculator to find log 10

  9. Natural logarithm • The natural logarithm is a log with base e. • Abbreviation is ln • loge5 will be written as ln 5 * “ln” means the base is understood to be e* What is the value of ln e?

  10. Some other important properties that always hold true: • loga1=0 • logaa=1 • logaax=x • ln1 = 0 • ln e = 1 • lnex=x

  11. Simplify. • log55x • 7log714 • log51

  12. If logax=logay, then x=y • Solve for x: log2x=log23 • Solve for x: log44= x

  13. Steps to graphing a logarithmic function • Rewrite as an exponential equation • Pick values for Y and solve for x • Plot the points.

  14. Graph y = log 2x • Rewrite as Exponential equation: ___________ • Domain: • Range: • Intercepts: • Asymptotes: • How is this related to the graph y =2x?

  15. Graph f(x) = log3x • Rewrite as an exponential equation: ___________________ • Domain: • Range: • Intercepts: • Asymptotes:

  16. Graph y = log 4 x • Rewrite as an exponential equation: ___________________ • Domain • Range • Intercepts • Asymtpotes

  17. Graph y = lnx • Rewrite as an exponential equation: ___________________ • Domain: • Range: • Intercepts: • Asymptotes:

  18. Graph y = log3(x-2) • Rewrite as an exponential equation: ___________________ • Domain: • Range: • Intercepts: • Asymptotes:

  19. Transformations • What happens to the graph of f(x±c)? Moves right or left c units • What happens to the graph of f(x) ± c? Moves the graph up or down c units • What happens to the graph of f(-x)? Reflects across the y axis • What happens to the graph of –f(x)? Reflects across the x axis

  20. Suppose f(x) = log2xDescribe the change in the graph • G(x) = log2(-x) Reflect over the y axis • G(x) = log2 (x+5) Moves 5 units to the left, VA: x = -5 • G(x) = -log2(x) Reflect over the x axis • G(x) = log2x-4 Moves the graph down 4 units • g(x) = log 2 (x-3) Moves the graph 3 units to the right, VA: x = 3

  21. Sketch the following graphsDon’t forget RXSRY • Y = -lnx 2. Y = ln(-x) • Y = ln(x-2) • Y = lnx + 3

More Related