Question

Let f(x) represent a function. Which descriptions match the given transformations? Drag and drop the answers into the boxes.  

f(x−3.5) -->


3.5f(x)-->

f(x)
is translated 3.5 units down.​
f(x)
​ is translated 3.5 units left.
f(x)
 is vertically compressed by a factor of 3.5.
f(x)
is translated 3.5 units up.​
f(x)
​ is vertically stretched by a factor of 3.5. 
f(x)
is  translated 3.5 units right.

Answer 1

3.5f(x) is vertically streched and f(x-3.5) is transaleted 3.5 units up

Explanation:

Answer 2

For f(x - 3.5) the answer is that f(x) is translated 3.5 units right

You can figure that out by thinking that for x = 3.5 (which is 3.5 units to the right of x = 0, f(3.5 - 3.5) is the same that f(0), ... for x = 10.5 (which is 3.5 units to the right of x = 7, f(10.5 - 3.5) = f(7) ... and so for every value of x.

For 3.5 f(x) the answer is that f(x) is vertically stretched by a factor of 3.5 which you figure out from a table like this:

f(x) 3.5 f(x)

0 0

1 3.5

2 7

10 35

And from that you can see the 3.5 f(x) is horizontally compressed and vertically stretched respect to f(x).