In Exercises 1-16, use the graph of y = f(x) to graph each function g.
g(x) = -f(x) +3

Key Concepts

Function Transformation

Function transformation refers to the changes made to the graph of a function through operations such as shifting, reflecting, stretching, or compressing. In this case, the function g(x) = -f(x) + 3 involves a vertical reflection across the x-axis due to the negative sign and a vertical shift upwards by 3 units.

Reflection Across the X-Axis

Reflecting a function across the x-axis means that for every point (x, y) on the graph of the function, the corresponding point on the reflected graph will be (x, -y). This transformation changes the sign of the output values, effectively flipping the graph over the x-axis, which is crucial for understanding how g(x) is derived from f(x).

Vertical Shift

A vertical shift occurs when a function is moved up or down on the graph without altering its shape. In the function g(x) = -f(x) + 3, the '+3' indicates that the entire graph of -f(x) is shifted upwards by 3 units, affecting the y-coordinates of all points on the graph, which is essential for accurately plotting g(x).