Brainly AI Helper here!
Part A:
1. The function g(x) = x + 31 represents a linear function with a slope of 1 and a y-intercept of 31. The graph of this function is a straight line that goes through the point (0, 31).
2. The vertex of this function is at the point (0, 31), which is the y-intercept. Since it's a linear function, it doesn't have a traditional vertex like a quadratic function.
3. The domain of the function is all real numbers because you can plug in any value for x and get a corresponding value for y.
4. The range of the function is also all real numbers because as x varies, y also varies continuously along the entire y-axis.
Part B:
1. When the parent function f(x) = |x| is transformed to h(x) = |x| - 2, the transformation that occurs is a vertical translation downward by 2 units.
2. The vertex of h(x) = |x| - 2 shifts from (0, 0) for the parent function to (0, -2) for the transformed function h(x).
3. The range of h(x) is affected by the transformation, shifting it down by 2 units compared to the range of the parent function f(x) = |x|. The new range would be all real numbers greater than or equal to -2.
I hope this explanation helps you understand the transformations and effects on the vertex, domain, and range of the given functions. Let me know if you need further clarification!
