Final answer:
A linear function can undergo various transformations such as vertical or horizontal shifts, stretching or compressing, and reflecting. These transformations are achieved by adjusting the equation of the linear function.
Step-by-step explanation:
A linear function is a function of the form y = mx + b, where m is the slope and b is the y-intercept. Transformations of a linear function can include shifting the graph vertically or horizontally, stretching or compressing the graph, or reflecting the graph across the x-axis or y-axis.
Here are some examples of transformations:
- Vertical shift: y = mx + b + c shifts the graph c units up or down.
- Horizontal shift: y = m(x - a) + b shifts the graph a units left or right.
- Stretch/compress: y = a(mx) + b stretches or compresses the graph vertically by a factor of a.
- Reflection: y = -mx + b reflects the graph across the x-axis.