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 left.f(x) is translated 3.5 units down.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

f(x−3.5) -> f(x) is translated 3.5 units right.

3.5f(x) -> f(x)​ is vertically stretched by a factor of 3.5.

Explanation:

Given some function f(x), for x = 0 it is associated f(0), for x = -3.5 it is associated f(-3.5) . Now, applying f(x−3.5) when x = 0 gives f(-3.5). Following the same procedure with all the other points the same happen, and f(x) is translated 3.5 units right.

Continuing with the same example, applying the transformation 3.5f(x) when x = 0 gives 3.5f(0), when x = 1 then the transformation results in 3.5f(1) . Following the same procedure with all the other points results in f(x) vertically stretched by a factor of 3.5.

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). so for overall the answer is

f(x - 3.5) f(x) is translated 3.5 units right

f(x) is vertically stretched by a factor of 3.5