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The graph of y = f(x), consisting of two line segments and a semicircle, is shown for -4 ≤ x ≤ 3. Sketch a...

12. The graph of y = f(x), consisting of two line segments and a semicircle, is shown for -4 ≤ x ≤ 3. Sketch a graph of m on the same axes above where m(x) = f(2x).
13. The domain of a function h is -4 ≤ x ≤ 7 and the range of h is -6 ≤ y ≤ 0. Find the domain and range of g, where g(x) = 3h(x - 2).
14. The domain of a function k is 2 ≤ x ≤ 14 and the range of k is -3 ≤ y ≤ 2. Find the domain and range of r, where r(x) = -2k(2x).
15. The domain of a function f is -6 ≤ x ≤ 4 and the range of f is -10 ≤ y ≤ 3. Find the domain and range of p, where p(x) = 5 - 3f(2(x + 1)).

Answer

12. To sketch the graph of m(x) = f(2x), compress the graph of f(x) horizontally by a factor of 2. This means the x-values will range from -2 to 1.5.

13.

  1. Domain of g: Since g(x) = 3h(x - 2), shift the domain of h by 2 units to the right. New domain: -2 ≤ x ≤ 9.
  2. Range of g: Multiply the range of h by 3. New range: -18 ≤ y ≤ 0.

14.

  1. Domain of r: Since r(x) = -2k(2x), compress the domain of k by a factor of 2. New domain: 1 ≤ x ≤ 7.
  2. Range of r: Multiply the range of k by -2. New range: -4 ≤ y ≤ 6.

15.

  1. Domain of p: Since p(x) = 5 - 3f(2(x + 1)), shift the domain of f by 1 unit to the left and compress by a factor of 2. New domain: -3.5 ≤ x ≤ 1.5.
  2. Range of p: Multiply the range of f by -3 and add 5. New range: -4 ≤ y ≤ 35.

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