Question

HELP ASAP PLSSSSS

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 V-shaped graph that opens upwards and has a vertex at x = 7. The vertex is the midpoint of the graph and occurs at the value of x where the absolute value changes from positive to negative. The domain of the function is all real numbers and the range is all non-negative numbers.

Part B:

The transformation from f(x) to h(x) occurs by shifting the graph of the parent function up by 2 units along the y-axis. In other words, every y-coordinate in the graph of f(x) is increased by 2 in the graph of h(x). The vertex of the parent function is (0,0) and is shifted to (0,2) in the transformed function. The range of h(x) is all non-negative numbers greater than or equal to 2.