Let g be a function that is a transformation of the function f such that g(x) = 1/2 f (x + 2) + 5. Describe...

1. Let g be a function that is a transformation of the function f such that g(x) = 1/2 f (x + 2) + 5. Describe the transformations of the function f that result with the function g.
2. Let k be a function that is a transformation of the function h such that k(x) = 4h (1/2 x) - 1. Describe the transformations of the function h that result with the function k.
3. Let r be a function that is a transformation of the function p such that r(x) = -3p(4x). Describe the transformations of the function p that result with the function r.
4. Let n be a function that is a transformation of the function m such that n(x) = 5 m(-x). Describe the transformations of the function m that result with the function n.
5. Let g(x) = f (x) - 3. Find the following values.
(a) g(-10)
(b) g(0)
6. Let h(x) = 4 - f (x - 2). Find the following values.
(a) h(2)
(b) h(6)
7. The function n is constructed by applying three transformations to the graph of h in this order: a horizontal dilation by a factor of 4, a vertical dilation by a factor of 2, and a vertical translation by 3 units. If h(x) = a(bx) + c, find the values of a, b, and c.
8. The graph of y = f (x), consisting of two line segments and a semicircle, is shown for -4 ≤ x ≤ 3. Sketch a graph of g on the same axes where g(x) = f (x - 2).
9. The graph of y = f (x), consisting of two line segments and a semicircle, is shown for -4 ≤ x ≤ 3. Sketch a graph of h on the same axes where h(x) = 2 f (x + 1).