IB DP Maths: AI HL复习笔记2.5.3 Stretches of Graphs

What are stretches of graphs?

• When you alter a function in certain ways, the effects on the graph of the function can be described by geometrical transformations
• For a stretch:
  • the graph is stretched about one of the coordinate axes by a scale factor
    • Its size changes
  • the orientation of the graph remains unchanged
• A particular stretch is specified by a coordinate axis and a scale factor:
  • The distance between a point on the graph and the specified coordinate axis is multiplied by the constant scale factor
  • The graph is stretched in the direction which is parallel to the other coordinate axis
  • For scale factors bigger than 1
    • the points on the graph get further away from the specified coordinate axis
  • For scale factors between 0 and 1
    • the points on the graph get closer to the specified coordinate axis
    • This is also called a compression

What effects do horizontal stretches have on the graphs and functions?

What effects do vertical stretches have on the graphs and functions?