Can someone please explain to me how to do these questions ? The coordinates of the maximum point of the graph y = f(x) are (4,3). Give the coordinates of the maximum point of the graph with equation: a) y = f(x), b) y = f(x) - 4, c) y = f(x-2) + 1?
This is a functions transformation question. What you need to know to solve this is how the addition or subtraction of a number, either within or outside of the function parentheses, i.e. f(x+...) or f(x)+..., affects the function. When you’re simply adding numbers to the function, you’re just causing a shift of the whole function in one direction. When you add or subtract a number within the parentheses, you cause a horizontal shift in the function, where adding a number means a shift to the left and adding a negative number means a shift to the right. When adding or subtracting a number to the whole function, i.e. outside the parentheses, you cause a shift in the vertical direction, and when you add a number you shift upwards and when you subtract a number you shift downwards. The answers to the questions above are therefore: a) Max at (4,3); this is simply the original function, no working is needed. b) Max at (4,-1); here you subtract 4 from the function so you shift the whole function 4 units downwards so the y coordinate changes from 3 to -1 and the x coordinate remains unaffected. c) Max at (6,4); here you subtract 2 inside the parentheses which results to a rightward shift of 2 units changing the x coordinate from 4 to 6 and then you add 1 to the whole function resulting in an upward shift of 1 unit changing the y coordinate from 3 to 4.
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