Answer:
The function g(x) = |x| - 5 is a translation of the parent function f(x), where the graph is shifted downwards by 5 units. The domain remains all real numbers, while the range is shifted downwards to y ≥ -5.
Explanation:
to understand how the transformation affects the domain and range. we got to see how the transformation affects the domain and range
1. Parent Function: The parent function f(x) = |x| represents the absolute value function. It has a "V" shape, with the vertex at the origin (0, 0). The domain of the parent function is all real numbers, and the range is all non-negative real numbers (y ≥ 0).
2. Translation: The function g(x) = |x| - 5 is a translation of the parent function f(x). The "5" in the equation represents a vertical shift downwards by 5 units. This means that the graph of g(x) will be the same as the graph of f(x), but shifted downwards by 5 units.
3. Effect on the Domain: The domain of g(x) remains the same as the parent function f(x), which is all real numbers. The translation does not affect the domain.
4. Effect on the Range: The range of g(x) is affected by the vertical shift. Since the parent function f(x) has a range of y ≥ 0, subtracting 5 from the function g(x) will shift the range downwards by 5 units. Therefore, the range of g(x) is y ≥ -5.