Questions concerning, logs, rational funtions, and trig.

[EasyStyle4747]

Allright, I have a math test next week and there's some things i want to clear up before i take it. I can't use a calculator btw.

1) We've learned a lot about testing symmetry (y-axis, x-axis, origin). It seems on most problems we just test y and origin symm. When do you know you shoudl test x-axis symm?

2) Ok, now for rational funtions. So you got the x and y intercepts figuired out. You got the vert and horizontal asymptotes. You got the symmetry figuired out. How do you graph it?? Ok, I know you put down the asymptotes as dotted lines, but how do you know on which side of the lines the curvy line goes on?

3) Trig equations: I have an example. Sin(theta)=1/2.
The answer is theta=pi/6+2k(pi) and 5(pi)/6+2k(pi) .
The problem is, some problems seem the have +k(pi) in the back instead of +2k(pi). How do you know when to use what? (Sorrie, i duno how to get the pi symbol out).

4) Ok, this might be so simple and easy but ok, Logs. I know how to the kinds of problems where its log(little 2)8. Like that represents 2^x=8, and the answer is 3. But what do you do when its just log1000, with no little number on the bottom. What does that mean? And same with ln1000, how do you do that. I punched it in the calculator and it gave me different answers from log1000.

5) Ok, this is just a problem with some weird instructions. Directions: solve. give exact answers- no calculators!
e^(3x-1)=5, 3^x=5, ln2x=8

Now i can simplify those fine. But give exact answers with no calculators?

6) Lastly, just look at this monstrosity: 2(log)(little 2)(x-1). How are u supposed to graph this without calculators?

please help, or this test is going to murder me!

 

[devious_]

1. You should always test for x-axis symmetry, just in case.

2. Find the range and domain of the function (i.e. the minimum values of y and x).

3. I'm not sure I follow.

4. ln1000 = log[e]1000, i.e. e^x = 1000
log1000 = log[10]1000, i.e. 10^x = 1000. A log with base 10 is usually written as lg or log (with no base).

5. I think by exact answer your teacher means no approximation.
e^(3x-1) = 5
3x-1 = ln5
x = (ln5+1)/3 -- Stop there. This is an exact answer.

6. You should know the graph of general log functions.
Let f(x) = log[n]x, try n=2, n=3, n=4, etc. And see how they differ.

In your question:
y=2log[2](x-1)
Find the x-intercept (y=0):
0 = log[2](x-1)^2
1 = (x-1)^2
x-1 = 1
x=2
Now..
y=2log[2](x-1) is actually a multi-transformation of y=log[2]x in the form of:
f(x) -> A*f(x) and f(x) -> f(x-a), you should know how to compute such transformations.

 

[EasyStyle4747]

ok I am still confused about one part in number 6. How did you go from 0 = log[2](x-1)^2 to 1 = (x-1)^2 ? How did the log[2] disappear? WHered the 1 come from?

And also one more thing, you said to know the graph of the th general log functions.
for this: f(x) = log[n]x, how can i punch that into my ti-89 graphing calculator? Like, i mean the [n] part.

 

[devious_]

Use a number instead of n. Try the following numbers: 2, 3, 4 and 5. This should help you get a general feel of how a log curve looks like.

Now,
0 = log[2](x-1)^2
Using the laws of logarithms
2^0 = (x-1)^2, but 2^0=1 => 1 = (x-1)^2

Hope that helps.