6. Given the function f(x) = 7x determine the equation of a new function, g(x), that is reflected over the x-axis and then shifted 4 units down.
a. g(x) = 7x + 4
b. g(x) = -7x + 4
c. g(x) = 7x - 4
d. g(x) = -7x - 4

d. g(x) = -7x - 4

Step-by-step explanation:

If it is reflected over the x-axis, there is a negative sign to the x term.

There is a shift of 4 units, so it is -4.

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

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