1. ## 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.

2. ## Re: Functions help!

Originally Posted by Lilmissmimiboots
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.

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.

3. ## Re: Functions help!

Originally Posted by romsek
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?

4. ## Re: Functions help!

Originally Posted by Lilmissmimiboots
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 $x=8$