I need help with these transformations!!!?

Question

I am completely stumped by this assignment. If you could lend any help I would appreciate it...even a website would be nice!

Here is the assignment:

In the following chart, describe the Transformation: give the domain and range of the translated function. Let f(x) be a simple graph that illustrates the transformations easily and sketch the pre-image and the image for each.

FUNCTION.............CHANGE IN GRAPH.......DOMAIN.......RANGE
1. f(x)
2. g(x)=f(x-c)
3. r(x)=f(x+c)
4. j(x)=f(kx), k>1
5. m(x)=f(kx), 0 6. n(x)=k[f(x)], k<0
7. u(x)=k[f(x)], k>1
8. h(x)=k[f(x)], 0 9. p(x)=f(x)+c
10. o(x)=f(x)-c
11. Q(x)= I f(x) I
12. v(x)=f(-x)
13. s(x)=f(IxI)

Answer 1

I think they're saying, "pick a function for x and then work out all of the other functions given." If that's the case, be easy on yourself and let

f(x) = x

then #2 becomes

g(c) = f(x-c) = x-c

The transformation is shifting to the right (for positive c)

#3 is

r(x) = f(x+c) = x+c

and the transformation is shifting tothe left (for positive c)

To graph them, put

y = f(x) = x for the first
y = g(x) = x-c for the second
y = r(x) = x+c for the third

and so on. Then plug in a few values for x, calculate the corresponding y values and plot the (x,y) points in the usual way.


Doug

Answer 2

When you change the function, how does the graph change? For example, if y=x^2 is transformed to y=3(x^2), then the graph is "stretched" vertically by a factor of 3. If y=x^2 is transformed to y=(x-1)^2 then the vertex of the parabola (and hence the whole parabola) is moved over to (1,0) from (0,0).

etc.

Looking at the graph of the transformed function will tell you what you need to know about the new domain and range. After all, these things are just code for where the graph exists in x and y.