2. (a) Given the graphs of the functions f(x)=2* and g(x)=-x+1,sketch a graph of the combined function (a) y=f(g(x)) on the axes below. (b) y=g(f(x)) g 8 00 CO 6 4 2 _f -4 -3 -2 -1 0 1 2 3 4 -2 -4 -6 (b) 8 g- 16 4 2 -4 -3 -2 -1 0 1 2 3 4 -2 -4 -6

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Use the graphs of f(x) and g(x) to evaluate each expression or state that it is undefined. On the graph, f(x) is blue and solid, and g(x) is red and dashed. (a) (f+g)(4) (b) (g-f)(2) (c) (fg)(0) (d) A. (f+g)(4) = f (1)(-1) INU 1₂ -16 -8 16- 8- -8- -16- y A V X 16 (a) Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

Analyze and sketch the graph of f(x) = x4 − 12x3 + 48x2 − 64x

Graph the function f (x)=(x+1)^2-4 by starting with the graph of y=x^2 and using transformations​ (shifting, stretching/compressing,​ and/or reflecting).

Find real numbers a, b, and c so that the graph of the function f(x) = ax2 +bx + c contains the points (-1, -6), (1, 4), and (2, 0). Use this model to predict f(4).

Suppose the functions g and f are defined as follows. h (x) = -5+ 4x? g (2) = 4 – 9x (a) Find ()(-1) (b) Find all the value(s) that are NOT in the domain(4)

For the given functions f and g, find the requested function and state its domain. f(x) = *+2; g(x) %3D 3x 7x-9 7x -9 Find f - g. (f - g)(x) = +2: (-∞, 0) u (0, ∞) 4x +2 7x-9 %D (f - g)(x) = 3: -위 (우- {x)x * ) %D 7x -9 ? (f - g)(x) = 10x-2 7x -9 (f - g)(x) = 4x+2: 7x -9