in 15 and 16, suppose f(x)=|x|. Find a equation for the image of f under the transformation.
15. S(x,y)=(x/4,5y)
16. T(x,y)=(x+1,y)
To find the equation for the image of the function f(x) = |x| under a given transformation, we need to apply the transformation to the input variable x and then substitute this transformed value back into the original function.
Let's first consider each transformation separately:
15. S(x, y) = (x/4, 5y)
To find the equation for the image of f(x) = |x| under S, we need to substitute x/4 into the original function f(x) = |x|.
So, substituting x/4 for x in |x|, we get:
f(S(x, y)) = |x/4|
Therefore, the equation for the image of f(x) = |x| under S(x, y) = (x/4, 5y) is:
f(S(x, y)) = |x/4|
16. T(x, y) = (x+1, y)
Similarly, to find the equation for the image of f(x) = |x| under T, we need to substitute x+1 into the original function f(x) = |x|.
So, substituting x+1 for x in |x|, we get:
f(T(x, y)) = |x+1|
Therefore, the equation for the image of f(x) = |x| under T(x, y) = (x+1, y) is:
f(T(x, y)) = |x+1|
In summary, the equations for the images of the function f(x) = |x| under the given transformations are:
15. f(S(x, y)) = |x/4|
16. f(T(x, y)) = |x+1|