Answer:
Horizontally to the left by 4 units, vertically upward by 8 units. These transformations will move the entire graph of f(x) to a new position without changing the shape or characteristics of the graph itself.
Explanation:
First, let's break down the transformations step by step:
f(x+4): This means that we are shifting the graph of f(x) horizontally to the left by 4 units. When you replace x with (x+4) in the function, it shifts the graph to the left by 4 units. For example, if f(x) had a point (2, y), then f(x+4) will have the same y-value but at the point (2-4, y) = (-2, y). This horizontal shift does not change the shape of the graph, just its position.
f(x+4) + 8: After the horizontal shift, we are then adding 8 to the entire function. This shifts the graph vertically upward by 8 units. If we previously had a point (x, y), after this step, it will become (x, y+8). This vertical shift also does not change the shape of the graph, just its position.
So, the features of the function g(x) = f(x+4) + 8 are:
It is the graph of f(x) shifted horizontally to the left by 4 units.
It is the graph of f(x) shifted vertically upward by 8 units.
Overall, these transformations will move the entire graph of f(x) to a new position without changing the shape or characteristics of the graph itself.