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1.2 day 2 Transformations of Functions

1.2 day 2 Transformations of Functions. Page 12. The rules for shifting, stretching, shrinking, and reflecting the graph of a function make it easier to sketch functions by hand. Since we will be frequently using graphs in our study of calculus, we will do a quick review of those rules.

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1.2 day 2 Transformations of Functions

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  1. 1.2 day 2 Transformations of Functions Page 12

  2. The rules for shifting, stretching, shrinking, and reflecting the graph of a function make it easier to sketch functions by hand. Since we will be frequently using graphs in our study of calculus, we will do a quick review of those rules. If we know how to graph the “parent” graph of a function, then we can modify that graph to get the one we want.

  3. Example: Adding a positive number at the end moves the graph up.

  4. Example: Adding a constant to x inside the parentheses moves the graph to the left. The horizontal changes happen in the opposite direction to what you might expect.

  5. Example: Placing a coefficient in front of the function causes a vertical stretch. In this case, the graph goes up twice as fast.

  6. Example: If the coefficient is negative, then the graph is reflected about the x-axis.

  7. Example: Placing a coefficient inside the function in front of the x causes a horizontal shrink. In this case, the graph expands horizontally half as fast. The horizontal changes happen in the opposite direction to what you might expect.

  8. Example: Clearing the parentheses: In this case, a horizontal shrink is the same as a vertical stretch, but this is not always true.

  9. Example: If the coefficient inside the function in front of the x is negative, you get a reflection about the y axis. In this case, since we started with an even function, we cannot see the reflection. Let’s look at an odd function.

  10. Example: Placing a negative coefficient inside the function in front of the x causes a reflection about the y-axis.

  11. is a stretch. is a shrink. To summarize the rules for transformations of graphs: Vertical stretch or shrink; reflection about x-axis Vertical shift Positive d moves up. Horizontal shift Horizontal stretch or shrink; reflection about y-axis Positive c moves left. The horizontal changes happen in the opposite direction to what you might expect.

  12. Now let’s look at a more complicated example: vertical flip right three moves down half as fast up four p

  13. Homework 1.2b 1.2 p19 6,12,22,25,28,31,44,49

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