The graphs of exponential and logarithmic functions by Mariel Atregenio https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2 G12 IBDP MAA (September 15, 2021) en-us 2021-09-14 23:52:36 UTC 2025-01-27 20:07:01 UTC hello@padlet.com https://padlet.net/icons/png/1f9e9.png Collaborative Task (25 min) - Group 4 iteachmathsmariela https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1740939422 1.  As a group, create a mind map providing the following information: 
  • the properties and features of graphs of exponential functions,
  • why b is only positive in an exponential function y = b^x,
  • the properties and features of graphs of logarithmic functions, 
  • the difference between the logarithmic and square-root functions.

Click this link above to access your notes.

2.  Using GeoGebra, graph in the same grid each group of functions:
  •   y = 10^x, y = log x and y = x,
  •   y = e^x, y = ln x and y = x. 
Upload a screenshot of your work in the provided space.
What do you notice with each pair of graphs?
What is true for the functions y = 10^x and y = log x, and y = e^x and y = ln x? 
Write a generalization about y = a^x and y = log to the base a of x. 


]]> 2021-09-14 23:52:36 UTC https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1740939422 Exponential Functions iteachmathsmariela https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1740939423 2021-09-14 23:52:36 UTC https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1740939423 Logarithmic functions iteachmathsmariela https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1740939425 2021-09-14 23:52:36 UTC https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1740939425 The graphs of y = a raised to x, and y = log to the base a of x iteachmathsmariela https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741106038 2021-09-15 01:05:53 UTC https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741106038 First Group of Functions theresereyes https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741448119 2021-09-15 03:12:42 UTC https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741448119 Characteristics when the base is >1 biancaadzuara https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741472564
  • The graph passes through the point (0,1)
  • The domain is all real numbers.
  • The range is y>0.
  • The graph is increasing.
  • The graph is asymptotic to the x-axis as x approaches negative infinity.
    • - Bianca A.

    ]]>     2021-09-15 03:22:25 UTC https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741472564     Second Group of Functions theresereyes https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741473892 2021-09-15 03:22:57 UTC https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741473892 Logarithmic and exponential functions rociotrillo https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741475775 - they are inverses of each other
    - exponential function can be seen as ƒ(x) = ex
    -     logarithmic function is seen as g(x) = ln x

    - Rocio T.]]>     2021-09-15 03:23:45 UTC https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741475775     Exponential Growth and Decay biancaadzuara https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741480283
  • If the base, b, is greater than 
    1, then the function increases exponentially at a growth rate of b. This is known as exponential growth.
  • If the base, b, is less than 1 (but greater than 0) the function decreases exponentially at a rate of b. This is known as exponential decay.
    • - Bianca A.
    ]]>     2021-09-15 03:25:39 UTC https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741480283     Why b is only positive in an exponential function y = b^x https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741482165 The function y=b^x only takes on positive values, or outputs, because the x-axis is the horizontal asymptote.
    Jamin E. ]]>     2021-09-15 03:26:29 UTC https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741482165     e^x and ln(x) are inverses of each other theresereyes https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741482683 Looking at the functions, they mirror one another across the line y = x

    Thea R. ]]>     2021-09-15 03:26:42 UTC https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741482683     Logarithmic and square root functions rociotrillo https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741483332 - Both the square root and logarithmic functions have a domain limited to x values greater than 0
    -     The range of the square root function is all non-negative real numbers. 
    - The range of the logarithmic function is all real numbers.

    - Rocio T.]]>     2021-09-15 03:26:59 UTC https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741483332     Characteristics biancaadzuara https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741486425 - A logarithmic function will have the domain as (0, ∞). 
    - The range of a logarithmic function is (−∞, ∞). 
    - The logarithmic function graph passes through the point (1, 0). 
    - The graph of a logarithmic function has a vertical asymptote at x = 0.
    - Bianca A. ]]>     2021-09-15 03:28:21 UTC https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741486425     iteachmathsmariela https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741491229 You're doing a great job here, Group 4! Keep it up! :) ]]> 2021-09-15 03:30:26 UTC https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741491229 y = 10^x and y = log of x to the base 10 are inverses jaminesdicul https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741491507 - Looking at the graph, log of x to the base 10 is a reflection of 10^x
    - Reflection on the graph h : y = x

    Jamin E.]]>     2021-09-15 03:30:33 UTC https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741491507     y = a^x and y = log of x to the base a are inverses jaminesdicul https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741501596 2021-09-15 03:34:57 UTC https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741501596 Shows large increases/decreases in values because of a change in the value of x (exponent) theresereyes https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741502881 2021-09-15 03:35:32 UTC https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741502881 https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741518428 Very detailed, good job you're so talented]]> 2021-09-15 03:42:10 UTC https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741518428 iteachmathsmariela https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741531004 Good job, Group 4!]]> 2021-09-15 03:47:51 UTC https://padlet.com/iteachmathsmariela/522p0z539w0vaaz2/wish/1741531004