advertisement

TRANSFORMATIONS OF LINEAR FUNCTIONS The rules and what they mean: y f ( x ) This is our function y af ( x ) This is our function vertically stretched 1 y f ( x ) This is our function vertically compressed a y f (bx ) This is our function horizontally compressed 1 y f x This is our function horizontally stretched b y f ( x ) This is our function reflected over the x-axis y f ( x) This is our function reflected over the y-axis y f ( x c) This is our function with a horizontal shift right y f ( x c) y f ( x) d This is our function with a horizontal shift left y f ( x) d This is our function with a vertical shift down This is our function with a vertical shift up That’s a lot of rules… Now what?! Let’s apply the rules to move functions. y = 3x Let’s start with this function y = 3x shift the function horizontally right 3 horizontal movement will ALWAYS be inside with the x added or subtracted and is OPPOSITE what you want. To move the function horizontally, place the number inside parenthesis and do the opposite of the way you want to move. To move left put a plus and your number and to move right put a minus and your number. y = 3(x – 3) Let’s try some more! y = 3x horizontal shift left 4 y = 3(x + 4) y = 3x horizontal shift right 5 y = 3(x - 5) y = 3x horizontal shift left 7 y = 3(x + 7) But what about up and down? y = 3x shift the function vertically up 5 y = 3x + 5 just add on to the end. Remember up you need a + to move up and a – to move down. Vertical movements do EXACTLY what they say. y = 3x shift the function vertically down 2 y = 3x - 2 You try! y = 3x vertical shift up 3 y = 3x + 3 y = 3x vertical shift down 8 y = 3x - 8 Put them together! y = 3x vertical shift down 5 and horizontal shift right 6 y = 3(x – 6) – 5 Too easy? Let’s look at some others! Vertically stretch y = 3x by a scale factor of 2 Simply put the 2 on the outside of 3x like this: y = 2(3x) That’s it???? Yep, that’s it! But what if it is a compression? Same deal but you will see a fraction. Try it! Vertically compress y = 3x by a scale factor of 1/4 1 y 3 x 4 Horizontal compressions and stretches the number will be inside touching the x. If the number is a whole number it will COMPRESS If the number is a fraction it will STRETCH the function. y = 3x compress the function horizontally by a scale factor of 2 y = 3(2x) y = 3x stretch the function horizontally by a scale factor of 1/2 1 y 3 x 2 y = 3x reflect across the x-axis y = -3x y = 3x reflect across the y-axis y = 3(-x)