Practice Exponential Functions l

Jan 15, 2020
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For each exponential function, do A through D.

A. Find asymptote
B. Find domain
C. Find range
D. Find intercept(s)

20200211_034708.jpg
 

MarkFL

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Once you do A., you should observe that B is a reflection of A across the \(y\)-axis, and C is a reflection of A across the \(x\)-axis. :)
 
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Jan 15, 2020
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Once you do A., you should observe that B is a reflection of A across the \(y\)-axis, and C is a reflection of A across the \(x\)-axis. :)
Cool.
 

MarkFL

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Yep.
 
Jan 15, 2020
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Once you do A., you should observe that B is a reflection of A across the \(y\)-axis, and C is a reflection of A across the \(x\)-axis. :)
20200211_194519.jpg


20200211_194602.jpg


20200211_194618.jpg
 

MarkFL

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Looks good except for the range of the first one. :)
 

MarkFL

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\((0,\infty)\)
 

MarkFL

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Can't you use Desmos?
 

MarkFL

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Here is a plot of all 3 functions:

tml_0012.png


The one in bold red is \(y=e^x\). The one in green is \(y=e^{-x}\), which as I stated is a reflection of the original across the \(y\)-axis. The one in blue is \(y=-e^x\) which is a reflection of the original across the \(x\)-axis.
 
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Here is a plot of all 3 functions:

View attachment 1214

The one in bold red is \(y=e^x\). The one in green is \(y=e^{-x}\), which as I stated is a reflection of the original across the \(y\)-axis. The one in blue is \(y=-e^x\) which is a reflection of the original across the \(x\)-axis.
Interesting picture.

1. What is graphing good for in real life?

2. Why is graphing by hand not taught as much in grades 6 to 12 if it is truly important?

3. To me, Desmos solves the graphing problem. It is more important, in terms of exams leading to good paying jobs for young people fresh out of college, to "master" the skill of setting up equations when solving word problems. Do you agree? No one in a job interview will ask the applicant to graph y = sin x to get the job. See my point? Not even an applicant for a math teacher job will be asked to graph trig functions.

4. In 2006, I was not able to pass the Financial Advisor test for a job that would have certainly been far better than anything related to my current job. I was angry and full of bitterness that year. So, should I be more concerned about increasing my skills in terms word problems more than anything else in the world of math?