if f(x)= x+2, find the equation of the function F obtained by stretching the function f vertically by a factor of 2 and compressing the function horizontally by a factor of 2, followed by a translation of 1/2 horizontally and -3 vertically.
the equation is: -x^2 - 6x - 7
what happens to the points (0,2) and (-1,1) under the transformation? i don't know what to do/how to find the answer
To find the equation of the function F resulting from the given transformation, we need to go step by step.
Step 1: Stretch the function vertically by a factor of 2.
The equation becomes f(x) = 2(x+2).
Step 2: Compress the function horizontally by a factor of 2.
To compress the function horizontally by a factor of 2, we substitute x/2 in place of x. So, the equation becomes f(x) = 2((x/2)+2), which simplifies to f(x) = 2(x/2 + 1).
Step 3: Translate horizontally by 1/2 and vertically by -3.
To translate the function horizontally by 1/2, we replace x with (x - 1/2). To translate the function vertically by -3, we subtract 3 from the function.
Applying these transformations, the equation becomes:
F(x) = 2((x/2 + 1) - 1/2) - 3
Simplifying further, we get:
F(x) = x - 1 - 3
F(x) = x - 4
Now let's find out what happens to the points (0,2) and (-1,1) under this transformation.
Point (0,2):
We substitute x = 0 into the equation F(x) = x - 4:
F(0) = 0 - 4
F(0) = -4
So, the point (0,2) transforms to (-4, -3) under this transformation.
Point (-1,1):
We substitute x = -1 into the equation F(x) = x - 4:
F(-1) = -1 - 4
F(-1) = -5
So, the point (-1,1) transforms to (-5, -3) under this transformation.
In summary, under the given transformation, the point (0,2) transforms to (-4, -3) and the point (-1,1) transforms to (-5, -3).