transformation of graph of f(x) = log(x); asymptotes, interc

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koreywarren

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The assignment says:

Describe the transformation on the following graph of f(x) = log(x). State the placement of the vertical asymptote and x-intercept after the transformation.

g(x) = log(x-3) description of transformation, equations for the vertical asymptote, x-intercept in (x,y) form

g(x) = log(-x) description of transformation, equations for the vertical asymptote, x-intercept in (x,y) form

Again, I am totally lost. This post and the one before it are the only two I don't get. I can't seem to wrap my brain around what the professor wants!! Please Help!
 
koreywarren said:
I am totally lost.
Click to expand...
Are you needing lesson links on functions? Function notation? Translations / transformations of graphs? Asymptotes? Logarithms? Intercepts? Line equations? Or something else?

Please be specific. Thank you! :D

Eliz.
 
I don't know what I need. If I knew what I needed, I wouldn't be using this site. I'm just completely in dark here. I typed exactly what the assignment says verbatum. What should I do?
 
koreywarren said:
I don't know what I need.
Click to expand...
Oh, golly... You're not familiar with any of the listed topics...? :shock:

I'm afraid it sounds as though you were somehow mistakenly placed in the wrong course. (Unfortunately, placement tests do sometimes fail.) It sounds as though you need at least one or two courses that are prerequisite to the one you're taking. Please conference with your academic advisor as quickly as possible!

Eliz.
 
koreywarren said:
The assignment says:

Describe the transformation on the following graph of f(x) = log(x). State the placement of the vertical asymptote and x-intercept after the transformation.

g(x) = log(x-3) description of transformation, equations for the vertical asymptote, x-intercept in (x,y) form

g(x) = log(-x) description of transformation, equations for the vertical asymptote, x-intercept in (x,y) form

Again, I am totally lost. This post and the one before it are the only two I don't get. I can't seem to wrap my brain around what the professor wants!! Please Help!
Click to expand...

Please tell us the definitions of the following (either from your textbook or class notes):

transformation

vertical asymptote

x-intercept

if possible - with examples.
 
I believe the description of transformation of g(x) = log(x-3) is: graph of this function is a horizontal translation of the graph g(x) = log(x-3), move right 3 units. You can't take log of a negative number. You must find the value of x by (x-3)=0 so, x must = 3. That is the equation for the vertical asymptote x = 3. and the x-intercept in (x,y) form is (4,0) g(x) = log(x-3), 0 = log(x-3), 10^0 = 10^log(x-3), 1 = x-3, add +3 to both sides to get 4 = x
I believe the description of transformation of g(x) = log(-x) is: graph of this function is a reflection the graph of g(x) = log(x) in the x-axis. I had some else help me find those answers,however, we ran out of time and did not find the equation for the vertical asymptote or the x-intercept in (x,y) form.
 
koreywarren said:
I believe the description of transformation of g(x) = log(x-3) is: graph of this function is a horizontal translation of the graph g(x) = log(x-3), move right 3 units. You can't take log of a negative number. You must find the value of x by (x-3)=0 so, x must = 3. That is the equation for the vertical asymptote x = 3. and the x-intercept in (x,y) form is (4,0) g(x) = log(x-3), 0 = log(x-3), 10^0 = 10^log(x-3), 1 = x-3, add +3 to both sides to get 4 = x
I believe the description of transformation of g(x) = log(-x) is: graph of this function is a reflection the graph of g(x) = log(x) in the x-axis. I had some else help me find those answers,however, we ran out of time and

did not find the equation for the vertical asymptote or the x-intercept in (x,y) form.
Click to expand...

Finding these would not take any time - if you knew the definitions of those terms.

So to complete your understanding - please show us that you know those definitions.

If your text-book is no-help, search in google. It will help you a lot.
 
Hello Korey:

I'm glad you finished your assignment, but I'm concerned about two incorrect statements that you typed. You may want to review your results to make sure that you eventually corrected these two misconceptions.

koreywarren said:
... g(x) = log(x-3) is: graph of this function is a horizontal translation of the graph g(x) = log(x-3) ...

g(x) = log(-x) is: graph of this function is a reflection the graph of g(x) = log(x) in the x-axis.
Click to expand...

g(x) = log(x - 3) is a horizontal shift of log(x) to the right by three units, not a horizontal shift of log(x - 3).

g(-x) = log(-x) is a reflection of log(x) across the y-axis, not the x-axis. To reflect across the x-axis, the exercise would need to be g(x) = -log(x).

Cheers,

~ Mark :)

PS: Here is a warning if you have two translations to do and one of them is a relection across the y-axis and the other is a horizontal shift. Consider the following function.

f(x) = log(2 - x)

We factor a -1 from this function's argument in order to see the shift.

f(x) = log(-[x - 2])

Now we can see that there is a horizontal shift of log(x) to the right by 2 units and also a reflection across the y-axis.

Does it matter which translation you do first?

BE CAREFUL!
 
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