1. ## Functions (Transformations) help...

Question:
1. The graph of function g is made by applying the transformations listed below, in the given order, to the function f(x)√x. Find an equation for the function g.

· Shift to the right by 4 units
· Vertical stretch 1 units
· Reflection with respect to the x-axis

From what i understand g(x) = f(x)√x
Shift to the right by 4 units would be be g(x) = f(4)√4?
I'm a little confused as for the vertical stretch.... and for the reflection with respect to the x-axis i understand that f(x) would have to be a negative value...

Any help would be greatly appreaciated, thanks.

2. Originally Posted by irenavassilia
Question:
1. The graph of function g is made by applying the transformations listed below, in the given order, to the function f(x)√x. Find an equation for the function g.

· Shift to the right by 4 units
· Vertical stretch 1 units
· Reflection with respect to the x-axis

From what i understand g(x) = f(x)√x
Shift to the right by 4 units would be be g(x) = f(4)√4?
I'm a little confused as for the vertical stretch.... and for the reflection with respect to the x-axis i understand that f(x) would have to be a negative value...

Any help would be greatly appreaciated, thanks.

· Vertical stretch 1 units
I am not too sure but if this means that stretch factor is 1

than the final equation is
g(x) = -f(x-4)√(x-4)

__________________________________________________ _
Shift to the right by 4 units would be

g(x) = f(x-4)√(x-4)

for stretch factor mutiply everything by 1

ie ;
g(x) = -f(x-4)√(x-4)

_________________________________________________

3. Shift to the right by 4 units.
A "shift to the right" for a function say, $h(x)$ is $h(x-4)$.

In your case, $f(x) \sqrt{x}$ so a shift ot the right is $p(x)=f(x-4) \sqrt{x-4}$.

Vertical stretch 1 unit
Is this part correct? If you stretch something by a scale factor of one, it will just remain exactly the same.

This might be helpful: A vertical stretch on a function $p(x)$ by a scale factor of $a$ is characterised by $ap(x)$.

Reflection with respect to the x axis.
If I have a point $(x,\ q(x))$ then a reflection in the x axis will give me $(x, \ -q(x))$.

Therefore since we have $f(x) \sqrt{x}$, a reflection in the x axis will be $q(x)=-f(x) \sqrt{x}$.

When we combine this we get:

$g(x)=(q \ o \ p)(x)=-f(x)\sqrt{x-4}$

4. Originally Posted by Showcase_22
A "shift to the right" for a function say, $h(x)$ is $h(x-4)$.
So from what I understand if we are specifying a any shift to the right we are going into the negative range for x? Where as lets say the shift was to the left then we are going into the positive range for x i.e. $h(x)$ is [tex]h(x+4)

Originally Posted by Showcase_22
This might be helpful: A vertical stretch on a function $p(x)$ by a scale factor of $a$ is characterised by $ap(x)$.
I'm not quite sure if i understan the vertical stretch on a function...

5. Originally Posted by irenavassilia
So from what I understand if we are specifying a any shift to the right we are going into the negative range for x? Where as lets say the shift was to the left then we are going into the positive range for x i.e. $h(x)$ is [tex]h(x+4)

I'm not quite sure if i understand the vertical stretch on a function...
btw I suggest you should read this

6. Where as lets say the shift was to the left then we are going into the positive range for x i.e. is [tex]h(x+4)
Yes it is! =D

I'm not quite sure if i understand the vertical stretch on a function...
This is something explained well on the link ADARSH posted. Read through it and absorb the knowledge! =p

7. Ok, i think i get this.

So we have a shift to right by 4 units - this is horizontal shift (+4) therefore g(x) = f(x-(+4)) √ (x-(+4))
g(x) = f(x-4) √ (x-4)

If we have a vertical stretch by 2 units - vertical stretch is represented as an a in the equation y = a(x-h)^2 + k therefore in this case g(x) = 2(f(x -4) √ (x-4))?

If we have a reflecation this is going to flip the graph by adding a negative therefore g(x) = -(f(x - 4) √ (x - 4))

Finally when we put it all together we have:

g(x) = -2(f(x-4) √ (x-4)) ???? Please let me know if i'm on the right path, thanks a bunch!

8. Yes, that's right! =p