tailieunhanh - Sat - MC Grawhill part 44

Tham khảo tài liệu 'sat - mc grawhill part 44', ngoại ngữ, ngữ pháp tiếng anh phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 420 McGRAW-HILL S SAT Answer Key 3 Transformations Concept Review 3 1. y f x 5 . Although the 5 seems to suggest a shift to the left because when we subtract 5 from a number we move five units to the left on the number line this change actually shifts the graph to the right. To see why look back at the first two examples in Lesson 3 and pay particular attention to how the changed equations produce the individual points on the graph and how these points compare with the points on the original graph. It also may help to pick a simple function such as y x2 graph it by hand by choosing values for x calculating the corresponding values for y and plotting the ordered pairs and then graph y x 5 2 in the same way to see how the graphs compare. 2. y x2 5. Since the point x y is the reflection of x y over the x-axis reflecting any function over the x-axis simply means multiplying y by 1. This negates every term in the function. 3. It is the original graph after it has been flipped vertically and stretched vertically. The graph of y 4f x is a vertically stretched version of y f x that also has been reflected over the x-axis. Every point on y 4f x is four times farther from the x-axis as its corresponding point on y f x and is also on the opposite side of the x-axis. 4. Overall shape and maximum and minimum values. The graph of y f x 15 is simply the graph of y f x shifted to the left 15 units. It maintains the shape of the original graph and has the same maximum and minimum values. That is if the greatest value of y on y f x is 10 then the greatest value of y on y f x 15 is also 10. 5. Zeroes vertical lines of symmetry and x coordinates of maximum and minimum values. The graph of y 6f x is simply the graph of y f x that has been vertically stretched by a factor of 6. Imagine drawing the graph of y f x on a rubber sheet and then attaching sticks across the top and bottom of the sheet and pulling the sheet until it s six times as tall as it was originally. The stretched graph .