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Math Help - Functions help!

  1. #1
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    Functions help!

    I need help solving a few questions in relation to functions. I would greatly appreciate if someone could explain the steps in how to solve each and not just give me the answer . The first equation is:

    1. Given the function f(x)={2x+1, x<2
    {X2 , 2 <_( less than or equal) x < 5. Find f(0), f(3), f(8)
    {3x-2, x >_(greater than or equal) 5.


    2. Find the function that shifts f(x)= X5three units to the left and 4 units down.

    3. If P=2xy and y= 3x+2, express P as a function of X.

    thanks for your help!!!
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  2. #2
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    Re: Functions help!

    Quote Originally Posted by Lilmissmimiboots View Post
    I need help solving a few questions in relation to functions. I would greatly appreciate if someone could explain the steps in how to solve each and not just give me the answer . The first equation is:

    1. Given the function f(x)={2x+1, x<2
    {X2 , 2 <_( less than or equal) x < 5. Find f(0), f(3), f(8)
    {3x-2, x >_(greater than or equal) 5.


    2. Find the function that shifts f(x)= X5three units to the left and 4 units down.

    3. If P=2xy and y= 3x+2, express P as a function of X.

    thanks for your help!!!

    1)
    I think you mean

    $f(x)=\left\{ \begin{array}{lr} 2x+1 &x<2 \\ x^2 &2 \leq x < 5 \\ 3x-2 &5 \leq x\end{array}\right.$

    just apply this to each of your values you have to find $f(x)$ for. For example

    $0 < 2 \Rightarrow f(x) = 2(0)+1 = 1$

    $2 < 3 < 5 \Rightarrow \dots$ (dots mean you can figure this out)

    $5 < 8 \Rightarrow \dots$

    2) In general f(x-a)+b shifts f(x) a units right and b units up. You can solve it from here.

    3) Just substitute what y equals into your expression for P and simplify.
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  3. #3
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    Re: Functions help!

    Quote Originally Posted by romsek View Post
    1)
    I think you mean

    $f(x)=\left\{ \begin{array}{lr} 2x+1 &x<2 \\ x^2 &2 \leq x < 5 \\ 3x-2 &5 \leq x\end{array}\right.$

    just apply this to each of your values you have to find $f(x)$ for. For example

    $0 < 2 \Rightarrow f(x) = 2(0)+1 = 1$

    $2 < 3 < 5 \Rightarrow \dots$ (dots mean you can figure this out)

    $5 < 8 \Rightarrow \dots$

    2) In general f(x-a)+b shifts f(x) a units right and b units up. You can solve it from here.

    3) Just substitute what y equals into your expression for P and simplify.
    Where do you get =1 in problem #1??? Does that mean that the second function would =5?
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  4. #4
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    Re: Functions help!

    Quote Originally Posted by Lilmissmimiboots View Post
    Where do you get =1 in problem #1???
    0 is less than 2 so

    $f(x)=2x+1$

    letting $x=0$ we get

    $2(0)+1=0+1=1$

    Does that mean that the second function would =5?
    No. You have to pick the right formula based on where x is in relation to 2 and 5

    $2 < 3 < 5$ so $f(x) = x^2$ for $x=3$

    $5 < 8$ so $f(x)=3x-2$ for $x=8$
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