Expert: Paul Klarreich - 8/21/2009

Question

"I have five questions for you. I am in the process of taking pre calculus, but cannot find the explanations to these questions in my book. I am not having trouble in other topics, but do not know how to get to the correct answers here. I have had a lot of SAT practice and scored 710, but I am stumped on these.Please explain how to get the answers to me so I can do other problems like these. I do need the answers very soon as my test is in two days. Many thanks!

1. Which equation represents y as a function of x? Why? I know that c is the correct answer, as I can solve for y, but what I do not understand is why d and b are incorrect.)
a. x=10    b. sinx +ye4= 6 c. y-6xe3=7x  d. 3x=ye2

2 If sin x = -3/5, then cos (2x) = ? Not sure how to start this one.

3. The expression log4(xe3square root of y) is equivalent to what equation? (I have not gotten to this type of question in my study of precalc yet, but this is a sample of the question on my test. Can you help me find an equivalent equation?

4. The solution set of the equation xe2-6x+7= 2 is
a. [0,-4,-2]   b. [1,3,5]  c. [-2,-1]  d. [2,4,6]
I think the answer is b, but dont' see how 3 works.

5. If f(x) =xe2-3x+4, then f(x+2)-f(2)=?
I have tried working this out, but never get the correct answer.


Answer
Questioner: Hayley
Country: United States
Category: Calculus
Private: No
Subject: Pre Calculus/Calculus
Question:
"I have five questions for you. I am in the process of taking pre calculus, but cannot find the explanations to these questions in my book. I am not having trouble in other topics, but do not know how to get to the correct answers here. I have had a lot of SAT practice and scored 710, but I am stumped on these.Please explain how to get the answers to me so I can do other problems like these. I do need the answers very soon as my test is in two days. Many thanks!

1. Which equation represents y as a function of x? Why? I know that c is the correct answer, as I can solve for y, but what I do not understand is why d and b are incorrect.)
a. x=10    b. sinx +ye4= 6 c. y-6xe3=7x  d. 3x=ye2

The correct answer is: none of them.  But if you word the question correctly, as "which equation can be solved for y as a unique function of x?" then:

a. cannot be solved; its graph is a vertical line.
b,d, result in  y = plus-or-minus something -- a no-no.


2 If sin x = -3/5, then cos (2x) = ? Not sure how to start this one.

Start by saying using the formula for cos(2x) = 1 - 2 sin^2(x):

Then you'll be OK.


3. The expression log4(xe3square root of y) is equivalent to what equation? (I have not gotten to this type of question in my study of precalc yet, but this is a sample of the question on my test. Can you help me find an equivalent equation?

You mean:  log4(xe3square root of y) is equivalent to what EXPRESSION?
Write log4(x^(3 sqrt(y)) = 3 sqrt(y) log4(x)

4. The solution set of the equation x^2-6x+7= 2 is
a. [0,-4,-2]   b. [1,3,5]  c. [-2,-1]  d. [2,4,6]

I think the answer is b, but dont' see how 3 works.
None of these look right.

5. If f(x) = x^2 - 3x + 4, then f(x+2)-f(2)=?
I have tried working this out, but never get the correct answer.

Do it SLOWLY.

First:

f(    ) = (    )^2 - 3(    )  + 4
f(x + 2) = (x + 2)^2 - 3(x + 2)  + 4
f(x + 2) = x^2 + 4x + 4  - 3x - 6  + 4
f(x + 2) = x^2 + x + 2

Then:
f(    ) = (    )^2 - 3(    )  + 4
f(  2 ) = (  2 )^2 - 3(  2 )  + 4
f(  2 ) = 4 - 6  + 4
f(  2 ) = 2

And finally,

f(x+2)-f(2) = x^2 + x + 2 - 2 = x^2 + x