Vertical compression-- I assume I only multiply the Y values?

[mickey222]

The problem is this: draw the graph y=-2f(x-3)-5.

I've gone about this by doing the following:

1. I understand the graph of y=(x-3)-5 to be linear, and the table of values look like this:

x y
0 -8
1 -7
2 -6
3 -5
4 -4
5 -3




2. the -2f refers to a vertical compression, and based on what I've been able to find, the -2 is multiplied only by the Y values, so that the X values are left alone, and you reach the following values:

x y
0 16
1 14
2 12
3 10
4 8
5 6

Have I got this right?

 

[skeeter]

[MATH]y=-2\cdot f(x-3) - 5[/MATH]
the transformations depend on the parent function, [MATH]f(x)[/MATH]
so, what is [MATH]f(x)[/MATH] ?

 

[Dr.Peterson]

The problem is this: draw the graph y=-2f(x-3)-5.

I would guess that the problem tells you what the function f is by showing its graph. What you graphed has nothing to do with the problem, because you ignored f entirely.

You'll need to find that graph and (a) try to use it to answer the question, and (b) show it to us so we can either confirm your answer or help you along.

 

[Steven G]

[math]f(x-3) \neq (x-3)\ unless\ f(x) = x.[/math] Did you forget to tell us this fact or maybe you failed to share the graph with us. In the end I assure you that you forget to tell us something or the problem is not a valid one.

 

[Steven G]

For the record (x-3) - 5 = x - 8

BTW, what happened to only multiplying the y value??

 

[mickey222]

Okay, I was confused as well, but it turns out we were only given the second half of the problem by accident. Here is the full problem:


Graph this ^

Then graph: y=-2f(x+3)-5
*** the real problem is x+3, not minus.

To graph the first, I plugged in X values, got their outputs, and the lines in black are the result. For the second part of the problem, I began by subtracting each value by 3, for as far as I understand, because +3 denotes a shift to the left, this is what must be done. Then, I multiplied each value by -2, and afterward, subtracted -5 from that Y value. The resulting lines of the transformation are thus shown in red.

One example of my math is this coordinate from f(x)=2x+7 , which was (-1,5). After transforming this particular coordinate, I ended up with (-4, -15).
Pursuant to y=-2f(x+3)-5, I took the X value -1, and subtracted it by 3 to reach -4. Then I multiplied the Y value 5 by -2, then subtracted that value by -5, and got -15.

 

[skeeter]

transformed graph looks fine to me