The graphs of exponential and logarithmic functions by Mariel Atregenio

Collaborative Task (25 min) - Group 3

iteachmathsmariela — 2021-09-14 23:51:23 UTC

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.

Exponential Functions

iteachmathsmariela — 2021-09-14 23:51:23 UTC

Logarithmic functions

iteachmathsmariela — 2021-09-14 23:51:23 UTC

The graphs of y = a to the x, and y = log to the base a of x

iteachmathsmariela — 2021-09-15 01:07:54 UTC

2021-09-15 03:18:01 UTC

Red - y = x
Green - y = 10^x
Blue - y = logx

Why b is only positive

nathanyu1 — 2021-09-15 03:18:04 UTC

the root of a negative number is imaginary

Properties of exponential functions:

2021-09-15 03:18:28 UTC

The x-axis is always an asymptote- Noelle

Properties of exponential functions:

2021-09-15 03:19:38 UTC

Decreasing line if 0 < a < 1
and increasing if a>1 - Noelle

logb(x) x-intercept

cristinarebanal — 2021-09-15 03:20:41 UTC

where b is a positive real number
x-intercept at (1,0)

- Tina R.

2021-09-15 03:21:16 UTC

Red - y = x
Green - y = e^x
Blue - y = lnx

logb(x) asymptotes

cristinarebanal — 2021-09-15 03:22:31 UTC

x=0 or the y-axis

- Tina R.

logb(x) domain

cristinarebanal — 2021-09-15 03:23:29 UTC

all positive real numbers

- Tina R.

logb(x) range

cristinarebanal — 2021-09-15 03:24:13 UTC

all real numbers

- Tina R.

similarity and difference with square root function

cristinarebanal — 2021-09-15 03:29:30 UTC

logb(x) same domain with √x

but log(x) has a vertical asymptote, the y-axis
- as x gets closer to 0
- y extended to negative infinity
- so does not have a minimum y-value

√x has a minimum y-value at 0

- Tina R.

iteachmathsmariela — 2021-09-15 03:29:48 UTC

You're doing a great job here, Group 3! Keep it up! :)

generalization about corresponding exp and log functions: inverses of each other

cristinarebanal — 2021-09-15 03:33:30 UTC

y = a^x and log to the base a of x

- Tina R.

2021-09-15 03:34:30 UTC

If the base b, is greater than 1, then the function increases exponentially at a growth rate of b. - Noelle

2021-09-15 03:36:33 UTC

If the base b is less than 1 (but greater than 0), the function decreases exponentially at a rate of b. (Exponential decay) - Noelle

iteachmathsmariela — 2021-09-15 03:46:33 UTC

Good job, Group 3!