Afunction is given. determine the average rate of change of the function between the given values of the variable. f(x) = 3 − x2; x = 2, x = 2 + h

Average rate of change is SLOPE: m = (y₂ - y₁)/(x₂ - x₁)

f(2) = 3 - (2)²

    = 3 - 4

    = -1

coordinate: (2, -1)

f(2 + h) = 3 - (2 + h)²

           = 3 - (4 + 4h + h²)

           = -h² - 4h - 1

coordinate: (2 + h, h² + 4h - 1)

m = (y₂ - y₁)/(x₂ - x₁)  = (-1 - (h² - 4h - 1)/(2 - (2 + h))  = (-h² + 4h)/-h = h - 4

h - 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

source:

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step-by-step explanation: