In Exercises 17-32, use the graph of y = f(x) to graph each function g.
g(x) = f(-x)+1

Function transformations involve altering the graph of a function through shifts, stretches, or reflections. In this case, the function g(x) = f(-x) + 1 represents a reflection of f(x) across the y-axis followed by a vertical shift upward by 1 unit. Understanding these transformations is crucial for accurately graphing the new function based on the original.

Reflecting a function across the y-axis means that for every point (x, y) on the graph of f(x), there is a corresponding point (-x, y) on the graph of f(-x). This transformation changes the sign of the x-coordinates while keeping the y-coordinates the same, which is essential for graphing g(x) = f(-x).

A vertical shift involves moving the entire graph of a function up or down without changing its shape. In the function g(x) = f(-x) + 1, the '+1' indicates that every point on the graph of f(-x) is moved up by one unit. This shift affects the y-coordinates of all points, which is important for determining the final position of the graph.