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

Question

Part B: If the parent function f(x) = |x| is transformed to h(x) = |x| + 3, 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 − 5| is a V-shaped graph with its vertex at (5,0). It opens upwards and has a y-intercept of (0,5). The domain of g(x) is all real numbers, because you can substitute any real value for x. The range of g(x) is all non-negative numbers, because the absolute value of a number is always non-negative.

Part B:

In the transformation of the parent function f(x) = |x| to h(x) = |x| + 3, a vertical shift occurs. The transformation is a vertical shift upwards by 3 units. The vertex of h(x) is shifted from (0,0) to (0,3). The range of h(x) is also affected by the vertical shift and becomes all non-negative numbers greater than or equal to 3.