The correct options are:
a) g(x) = 8*x - 6
b) g(x) = 2x - 10
c) g(x) = 2x - 14
d) g(x) = 8x - 24
<h3>
How to identify each transformation?</h3>
Here we have the function:
f(x) = 2x - 6
The proposed transformations are:
a) Stretch by a factor of 4 along the x-axis.
A horizontal stretch of scale factor k is written as:
g(x) = f(x*k).
Then, in this case, we have:
g(x) = 2(x*4) - 6 = 8*x - 6
b) Shift f(x) 4 units down.
A vertical shift of N units is written as:
g(x) = f(x) + N
A shift of 4 units down is written as:
g(x) = f(x) - 4 = 2x - 6 - 4 = 2x - 10
c) Shift f(x) 4 units right.
An horizontal shift of N units is written as:
g(x) = f(x + N).
For a shift of 4 units to the right, we write:
g(x) = f(x - 4) = 2(x - 4) - 6 = 2x - 8 - 6 = 2x - 14
d) A vertical compression of scale factor 1/4.
A vertical compression of scale factor K is written as:
g(x) = f(x)/K
In this case, we will have:
g(x) = f(x)/(1/4) = 4*f(x) = 4*(2x - 6) = 8x - 24
If you want to learn more about transformations:
brainly.com/question/4289712
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