# Thread: Very difficult problem (transformation of functions)

1. ## Very difficult problem (transformation of functions)

The problem states;
The graph of y=f(x) is given. Match each equation with its graph.
a) y=f(x-4)
b)y=2f(x+6)
c)y=f(x)+3
d)y=-f(2x)

What I find confusing is that these are parabolas. Why is this?

2. Originally Posted by ibrahimovic9
The problem states;
The graph of y=f(x) is given. Match each equation with its graph.
a) y=f(x-4)
b)y=2f(x+6)
c)y=f(x)+3
d)y=-f(2x)

What I find confusing is that these are parabolas. Why is this?
What are we matching these equations to? You don't have enough information here.

Given $y= f(x)$ is transformed to $y=a\times f(x-h)+k$

$a$ is a dilation factor away from the y axis, $h$ is a horizontal shift and $k$ a vertical shift.

3. sorry. Heres a link to a more descriptive analysis of the type of problem. Same instructions but different problem. It is problem number 4. The problem is in page 2.
http://www.farmingdale.edu/CampusPag..._Functions.pdf

http://www.farmingdale.edu/CampusPag..._Functions.pdf

4. Originally Posted by ibrahimovic9
The problem states;
The graph of y=f(x) is given. Match each equation with its graph.
a) y=f(x-4)
b)y=2f(x+6)
c)y=f(x)+3
d)y=-f(2x)

What I find confusing is that these are parabolas. Why is this?
The original graph of y=f(x) could be anything - in this case it is a parabola.

The question relates to transforming the original graph (whatever shape it is). There are basically 4 types of transformations:
y= a*f(x)
y=f(b*x)
y=f(x -c)
y=f(x) +d
The a, b, c, and d have different effects on the original graph of y=f(x).
Do you know what these effects are?

5. i dont know what these effects might be. The info I am giving you is the info shown to me. If you can see the link i posted. Appreciate all the help

6. Originally Posted by ibrahimovic9
i dont know what these effects might be. The info I am giving you is the info shown to me. If you can see the link i posted. Appreciate all the help
I can help you get a better understanding of this. Have you got a graphics calculator handy?

7. yes i do. I have typed in the equation y= f(x-4) but all i get is a straight line.

4 a) 2
b) ???
c) 1
d) 4

for 4 b) the equation is y = -f(x+4)

rearrange the equation become y = -f(x-(-4)) which is in standard form..

thus the graph of f(x) should be reflected across x-axis and shifted horizotally 4 unit to the left...

the graph for number 3 is -f(x+4)-1...

9. Originally Posted by ibrahimovic9
yes i do. I have typed in the equation y= f(x-4) but all i get is a straight line.
You need to understand what is going on here.
I think you probably typed in y=x-4 which IS a straight line, but that's irrelevant here.

I'll take you through the steps.
On your GC draw the parabola y=x^2 for starters. (You could do this with any graph but lets start with a basic parabola)

10. ok. i got that
next?

11. Originally Posted by ibrahimovic9
yes i do. I have typed in the equation y= f(x-4) but all i get is a straight line.
of course it will yield a straight line because you did nit define the function of f(x) is... since what you type is y= f(x-4) for sure it will sketch a straight line... try to the get the equation for the parabola shown in the figure... the substitute in the equation... the only you can sketch the parabola

12. Originally Posted by ibrahimovic9
ok. i got that
next?
Good, bear with me and you'll be an expert in no time!!

Keep the graph of y=x^2 and now also graph y=2*x^2. y=3*x^2

13. got it

14. Originally Posted by ibrahimovic9
got it
OK so what is the effect of multiplying by 2 and then 3. What happens to the original graph?

15. it shrinks

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