Given the parent function of f(x) = x4, what change will occur when the function is changed to -f(1/2x) ?

Graph opens the same way and is narrower

Graph opens the same way and is wider

Graph opens the opposite way and is narrower

Graph opens the opposite way and is wider

Question

Given the parent function of f(x) = x4, what change will occur when the function is changed to -f(1/2x) ?

 Graph opens the same way and is narrower

 Graph opens the same way and is wider

 Graph opens the opposite way and is narrower

 Graph opens the opposite way and is wider

mathslover · Answer

Is it f(x) = x^4 or f(x) = x4

$x^4 \ \text{OR}\  x4 \ ? $

anonymous · Answer

sorry yea its x^4

mathslover · Answer

Fine. So, you need to find $$ - f\left( \cfrac{1}{2x} \right) $$ 
Right?

anonymous · Answer

thats right just the x is right next to the line not on the bottom with the 2

mathslover · Answer

Oh Okay. That will make a bit difference in the final answer.

Now in order to find the above function in (1/ (2) * x ) .. then just plugin $ \cfrac{1}{2} x $ in place of $x$ in the parent function i.e. $f(x) = x^4 $

mathslover · Answer

For example, if you are require to find f(2) then you will just plugin x = 2 in the parent function i.e. 

$$ \boxed{ \mathsf{ f(x) = x^4 \\implies  f(2) = 2^4 \ \implies  f(2) = 16 } } $$ 

So, this is the way you will have to find $ - f\left( \cfrac{1}{2} x \right) $ 

Got it?

anonymous · Answer

yeah kinda so $$1/2^{4}$$ ?

mathslover · Answer

Not actually as you've ignored "x" there.

mathslover · Answer

See you have to plug in $\cfrac{1}{2} \times x $ at the place of just $x$ in the parent function. So, you will get something like thus: 

${ f\left( \cfrac{1}{2} x \right) = \left( \cfrac{1}{2} x \right)^4 } $

mathslover · Answer

Now, if you will solve it further, you will get: 

$\left( \cfrac{1 \times x^4 }{ 2^4} \right) $ 

which is equivalent to $\left( \cfrac{x^4}{2^4} \right) $ 

Right?

mathslover · Answer

See, why am I doing this all? Because this will help us to notice the changes in the graphs. 

I need you to give me some faster responses as I'm not here for much time.

anonymous · Answer

oh ok verry sorry i had to do something. but yes i am follwing what your saying

mathslover · Answer

Okay, now, notice that what I have found is $f \left( \cfrac{1}{2} x \right)$ , that is I have not taken negative till now.

Now, just take the negative of $\cfrac{x^4}{16}$ that is you get: 

$- f \left( \cfrac{1}{2} x \right) = - \cfrac{x^4}{16} $ 

$\color{blue}{\text{Originally Posted by}}$ @mathslover
See you have to plug in $\cfrac{1}{2} \times x $ at the place of just $x$ in the parent function. So, you will get something like thus: 

${\color{blue}{ f\left( \cfrac{1}{2} x \right)} = \left( \cfrac{1}{2} x \right)^4 } $
$\color{blue}{\text{End of Quote}}$

anonymous · Answer

ohh ok i get the steps now. so the graph opens the same way and wider

mathslover · Answer

Yeah, right. http://www.wolframalpha.com/input/?i=x%5E4+and+-+x%5E4+%2F+16 Notice the two graphs there, the graph of -x^4/16 will open the opposite way and wider (because of that 16 in the denominator)

mathslover · Answer

I hope this helped.

Good Luck!

anonymous · Answer

yes you help verry much. perfect job at explaining, thank you! (:

mathslover · Answer

Good to hear that Andy. Take care of yourself and good luck for future studies.

I wish you lots of good luck for your journey as a student all over the life as well as the journey on OpenStudy! 

(:

anonymous · Answer

thank you that was verry nice. i wish you the same! (:

anonymous · Answer

This is wrong, at least if you meant f(x)= x^4.  (just took the test)