Need some help with 3 Questions

[bellsouth]

Any help, response, or answers would be greatly appreciated!

The first one I am struggling with is this, 4 sqrt(x) + x = 1. You are supposed to solve the eqation algebraically.

The second one is, find the range of a function. f(x) = (x - 4)^2 + 4

The third one is,

Describe how to transform the graph of f into the graph of g.
f(x) = sqrt(x) and g(x) = - sqrt(x + 6)

A) Shift the graph of f left 6 units and then reflect across the x-axis.
B) Shift the graph of f right 6 units and then reflect across the x-axis.
C) Shift the graph of f up 6 units and then reflect across the y-axis.
D) Shift the graph of f left 6 units and then reflect across the y-axis.


I just cant seem to get anywhere started on each of these problems. I try to begin to solve them but end up in left field. Thanks again for any help.

 

[Loren]

\(\displaystyle 4\sqrt{x} + x = 1\)
\(\displaystyle 4\sqrt{x} = 1 - x\)
Now square both sides and go from there.

 

[stapel]

4 sqrt(x) + x = 1. You are supposed to solve the eqation algebraically.

Can you solve x[sup:2lzrt5qh]2[/sup:2lzrt5qh] + 4x - 1 = 0? If so, then use the same methodology, but solve for the square root of x, rather than for x. Then square to get the answers.

find the range of a function. f(x) = (x - 4)^2 + 4

The range is the set of y-values. So look at the graph (in particular, at the vertex), and copy down the range.

Describe how to transform the graph of f into the graph of g.
f(x) = sqrt(x) and g(x) = - sqrt(x + 6)

To learn about function transformations, try here. :wink:

 

[Loren]

find the range of a function. f(x) = (x - 4)^2 + 4

Can you plug in any value of x that would make the range zero?
Can you plug in any value of x that would make the range be less than 4?
Is there any way to make (x-4)[sup:mq19hsvf]2[/sup:mq19hsvf] negative so that f(x) would be a negative something + 4?

 

[bellsouth]

16sqrt(x^2) = 1 - 2x + x^2

 

[galactus]

\(\displaystyle \sqrt{x^{2}}=|x|\)

\(\displaystyle 16x=1-2x+x^{2}\)

and

\(\displaystyle -16x=1-2x+x^{2}\)

 

[bellsouth]

Thanks for the responses.

galactus, are you supposed to continue solving from there, or stop?

 

[galactus]

I don't know. What are your instructions?. I assume continue solving for x. Since we had an absolute value, there will be four solutions. Two for each quadratic.

Just use the quadratic formula.

 

[bellsouth]

Just supposed to solve the equation.

I could only get down to 18x-1-x^2=0

 

[bellsouth]

Would it be 9-4sqrt 5

 

[galactus]

Yes, that's one solution. There are 3 more.

Solve \(\displaystyle x^{2}-18x+1=0\)

and

\(\displaystyle x^{2}+14x+1=0\)

The solution you posted is one of the solutions for the first one.

 

[bellsouth]

Ok thanks.

How is this for the end.

4 sqrt(x) + x = 1
x=9-4sqrt5
x= 9+4sqrt5, 9-4sqrt5
x=-7+4sqrt3, -7-4sqrt3

 

[galactus]

There ya' go. To check your solutions, plug them back in and see if you get 0.

 

[bellsouth]

Ok I understand the first one now.

I am stil completely losssssssssssssssssssst on the final two.


What do you guys think?

Thanks

 

[stapel]

I am stil completely lost on the final two.

What do you guys think?

I think, from your response, that the hints, set-ups, lessons, and explanations provided here haven't been nearly enough. You apparently need instead to think about hiring a qualified local tutor who can work with you, face to face, teaching you the necessary background material, filling in whatever gaps are preventing you from comprehending the current course content. (We cannot teach courses within this environment, and the help we can provide isn't, you indicate, helping you at all, so the solution would not appear to be something that we can here provide.)

My best wishes to you in your studies.