Question

Question 4 (Essay Worth 10 points)

(02.05 HC)

Part A: Given the function g(x) = |x − 7|, describe the graph of the function, including the vertex, domain, and range. (5 points)

Part B: If the parent function f(x) = |x| is transformed to h(x) = |x| + 2, what transformation occurs from f(x) to h(x)? How are the vertex and range of h(x) affected?

Answer 1

Part A: The graph of the function g(x) = |x - 7| is a straight line with a vertex at (7, 0). The domain of the function is all real numbers, while the range is all real numbers greater than or equal to 0.

Part B: The transformation from f(x) = |x| to h(x) = |x| + 2 is a vertical shift upwards by 2 units. The vertex for the function h(x) is now at (0, 2), and its range is all real numbers greater than or equal to 2.