[بنووتة كيوت]

The graph of the function is given in blue. Use transformations to create the function whose graph is shown in red.
y = 4x − x2

y =
1





The graph of the function is given in blue. Use transformations to create the function whose graph is shown in red.

y =
1

The graph of the function is given in blue. Use transformations to create the function whose graph is shown in red.
y = 1



Find f g h.
f(x) = √x − 1
g(x) = x2
h(x) = x3 + 1
1



Express the function in the form f g. (Use only elementary functions, but not the identity function, g(x) = x.)

f (t) =
1


g(t) =
2



(a) If g(x) = 3x + 2 and h(x) = 9x2 + 12x + 6, find a function f such that f g = h. (Think about what operations you would have to perform on the formula for g to end up with the formula for h.)
f =
1



(b) If f(x) = 2x + 8 and h(x) = 2x2 + 2x + 6, find a function g such that f g = h.
g(x) =
2




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