# PracticeExponential Functions l

#### pre-trip_rapture

##### Member
For each exponential function, do A through D.

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

#### MarkFL

##### La Villa Strangiato
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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.

pre-trip_rapture

#### pre-trip_rapture

##### Member
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.

Staff member
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Math Helper
Yep.

#### pre-trip_rapture

##### Member
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.

#### MarkFL

##### La Villa Strangiato
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Looks good except for the range of the first one.

#### pre-trip_rapture

##### Member
Looks good except for the range of the first one.
What the range of y = e^x?

#### MarkFL

##### La Villa Strangiato
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$$(0,\infty)$$

#### pre-trip_rapture

##### Member
$$(0,\infty)$$
Can you show me why this is the range of y = e^(x) via a Desmos graph?

#### MarkFL

##### La Villa Strangiato
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Can't you use Desmos?

#### pre-trip_rapture

##### Member
Can't you use Desmos?
Yes, I know how to use Desmos. I just don't know how to copy and paste the picture here.

#### MarkFL

##### La Villa Strangiato
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Here is a plot of all 3 functions:

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.

pre-trip_rapture

#### pre-trip_rapture

##### Member
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?