# Thread: Functions and Transformations Project.

1. ## Functions and Transformations Project.

Hi guys! i'm new here at the forum. just got a math project on functions and transformations, but had some problems with the last part. so i need some urgent help as i have 2 more days untill the project is due. so here we go:

we were given a basic function f(x)=x^2. we were told to graph it and compare it to the graphs of various other functions. we were also asked to deduce the graphs and produce a table of results. so here is what i came up with:

Type of Transformation
Effect on Graph of f(x)
1
f(x) +c , c > o
upward shift by c

2
f(x) +c , c < o
downward shift by c

3
f(x + c), c >0
horizontal shift to left by c

4
f(x + c), c < 0
horizontal shift to right by c

5
-f(x)
reflection in x axis

6
f(-x)
reflection in y axis

7
α f(x), α > 1
vertical stretch by a

8
α f(x), 0 < α < 1
vertical compression by a

9
fx), α > 1
horizontal compression by a

10
fx), 0 < α < 1
horizontal stretch by a

now ill just post the final part from the project:

Part VIII

In this final part of the Project you and your group members are to use the knowledge gained from Parts I-VII to apply the rules of functional transformations to a function γ(x) where the formula is not known, but the graph ofγ(x) is known. On the last page of the lab is the graph of a function γ(x) for which the algebraic formula is unknown. Using the information gained in this lab, draw the graph of a new function β(x) defined according to β(x) = 1/2(1 - γ(-2x)) + 1.
Be sure to fully explain your reasoning in deducing the graph of β(x) in your final lab report.

now from my understanding, i have to transform the graph given above using the formula for b(x) above. but the formula is just so complicated that i cant understand what i need to do. any help will be greatly appreciated.

2. Originally Posted by satish555
Hi guys! i'm new here at the forum. just got a math project on functions and transformations, but had some problems with the last part. so i need some urgent help as i have 2 more days untill the project is due. so here we go:

we were given a basic function f(x)=x^2. we were told to graph it and compare it to the graphs of various other functions. we were also asked to deduce the graphs and produce a table of results. so here is what i came up with:

Type of Transformation
Effect on Graph of f(x)
1
f(x) +c , c > o
upward shift by c

2
f(x) +c , c < o
downward shift by c

3
f(x + c), c >0
horizontal shift to left by c

4
f(x + c), c < 0
horizontal shift to right by c

5
-f(x)
reflection in x axis

6
f(-x)
reflection in y axis

7
α f(x), α > 1
vertical stretch by a

8
α f(x), 0 < α < 1
vertical compression by a

9
fx), α > 1
horizontal compression by a

10
fx), 0 < α < 1
horizontal stretch by a

now ill just post the final part from the project:

Part VIII

In this final part of the Project you and your group members are to use the knowledge gained from Parts I-VII to apply the rules of functional transformations to a function γ(x) where the formula is not known, but the graph ofγ(x) is known. On the last page of the lab is the graph of a function γ(x) for which the algebraic formula is unknown. Using the information gained in this lab, draw the graph of a new function β(x) defined according to β(x) = 1/2(1 - γ(-2x)) + 1.
Be sure to fully explain your reasoning in deducing the graph of β(x) in your final lab report.

now from my understanding, i have to transform the graph given above using the formula for b(x) above. but the formula is just so complicated that i cant understand what i need to do. any help will be greatly appreciated.

Draw a diagram for each of these steps.

$\gamma(-x)$ is your reflection in the y-axis.

$\gamma(-2x)$ is your horizontal compression.

$-\gamma(-2x)$ is a reflection in the x-axis.

$1 - \gamma(-2x)$ is a vertical shift upwards by 1 unit.

$\frac{1}{2}[1 - \gamma(-2x)]$ is vertical compression.

$\frac{1}{2}[1 - \gamma(-2x)] + 1$ is a vertical shift upwards by 1 unit.

3. Originally Posted by satish555
Hi guys! i'm new here at the forum. just got a math project on functions and transformations, but had some problems with the last part. so i need some urgent help as i have 2 more days untill the project is due. so here we go:

we were given a basic function f(x)=x^2. we were told to graph it and compare it to the graphs of various other functions. we were also asked to deduce the graphs and produce a table of results. so here is what i came up with:

Type of Transformation

Effect on Graph of f(x)

1

f(x) +c , c > o

upward shift by c

2

f(x) +c , c < o

downward shift by c

3

f(x + c), c >0

horizontal shift to left by c

4

f(x + c), c < 0

horizontal shift to right by c

5

-f(x)

reflection in x axis

6

f(-x)

reflection in y axis

7

α f(x), α > 1

vertical stretch by a

8

α f(x), 0 < α < 1

vertical compression by a

9

fx), α > 1

horizontal compression by a

10

fx), 0 < α < 1

horizontal stretch by a

now ill just post the final part from the project:

Part VIII

In this final part of the Project you and your group members are to use the knowledge gained from Parts I-VII to apply the rules of functional transformations to a function γ(x) where the formula is not known, but the graph ofγ(x) is known. On the last page of the lab is the graph of a function γ(x) for which the algebraic formula is unknown. Using the information gained in this lab, draw the graph of a new function β(x) defined according to β(x) = 1/2(1 - γ(-2x)) + 1.
Be sure to fully explain your reasoning in deducing the graph of β(x) in your final lab report.

now from my understanding, i have to transform the graph given above using the formula for b(x) above. but the formula is just so complicated that i cant understand what i need to do. any help will be greatly appreciated.

Try breaking it up into "pieces" (that way you may better explain what is going on..using previous knowledge).

4. thanx a lot guys! really helpful.