Unit 2 Transformations
A one-page cheat sheet on Graph Transformations, covering summarized theory and the most important formulas. Free Download (PDF)
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You should have seen some graph transformations before, such as translations and reflections - recall that reflections in the x x -axis flip f (x) f (x) vertically and reflections in the y y -axis flip f (x) f (x) horizontally. Here, we will also look at stretches. There are 4 main types of graph transformation that we will cover.
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Transformations of Graphs Vertical and Horizontal Shifts of Graphs Reflecting, Stretching, and Shrinking of Graphs Combining Transformations Vertical and Horizontal Shifts of Graphs Graphs of Some Basic Functions: Vertical Shifts of Graphs: Horizontal Shifts of Graphs: Example: Solution: Example: Solution: Additional Example 1:
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TRANSFORMATION RULES Let f(x) be the original function and let c > 0, k > 0 be real numbers. Notice that a horizontal stretch is the same as a vertical shrink, and a horizontal shrink is the same as a vertical stretch. Figure 1: Vertical Stretch or Horizontal Shrink Figure 2: Vertical Shrink or Horizontal Stretch csusm.edu/stemsc XXXX @csusm_stemsc
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1. Functions & Graphs - Worksheets 2. About Graph Transformations 3. Functions & Graphs - Videos, Theory Guides & Mind Maps 4. Higher Maths Essential Skills 5. Higher Maths Exam Worksheets by Topic 6. Higher Maths Past & Practice Papers by Topic 7. Higher Maths Videos, Theory Guides, Mind Maps & Worksheets 8. Higher Maths Past & Practice Papers
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The graph of the new function is easy to describe: just take every point in the graph of f (x), and move it up a distance of d. That is, if (a, b) is a point in the graph of f (x), then (a, b + d) is a point in the graph of f (x) + d. As an explanation for what's written above: If (a, b) is a point in the graph of f (x), then that means f (a) = b.
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To do this we need to solve the quadratic equation of ++ − 2 2 + ( − 2) = ( = 0 − 1 =0 3 2 = 0 + 2)( − 1) = 0 +2 =0 Hence the roots of the function are at: =0 = 1 = −2 At coordinates (0,0), (1,0) & (−2,0) are where the x intercepts will be located. The same method can be applied to sketching graphs of quartic functions.
Notes Transformations of Parent Graphs
Graph transformations involve performing transformations such as translations and reflections on the graph of a function. In GCSE mathematics you may be asked to sketch a graph after a given transformation, or asked to write down the position of a coordinate after a transformation has been applied.
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This cheat sheet covers the high school math concept - Graph Transformations. This concept is a part of Calculus and is generally covered along with functions. A good knowledge of basic functions and their domains and ranges is a must to understand graphs and their transformations.
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Function Transformations. Transformation of functions means that the curve representing the graph either "moves to left/right/up/down" or "it expands or compresses" or "it reflects". For example, the graph of the function f (x) = x 2 + 3 is obtained by just moving the graph of g (x) = x 2 by 3 units up. Function transformations are very helpful.
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A Function Transformations reference sheet. Since I never miss a change to procrastinate, I decided to spend some time compiling a "cheat sheet" for function transformations. I've included the following 8 transformations: A constant added to or subtracted from a function shifts its graph vertically. A constant added to or subtracted from a.
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The function transformation cheat sheet contains a written description of each transformation, what it looks like in function notation, and what visually happens to the graph. (The parent absolute value function, f(x) = |x| was utilized for the visual as all of the transformations are crisp and clear).
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VARIATIONS OF SINE AND COSINE FUNCTIONS. Given an equation in the form f(x) = A sin(Bx − C) + D or f(x) = A cos(Bx − C) + D, C B is the phase shift and D is the vertical shift. Example 2.4.3: Identifying the Phase Shift of a Function. Determine the direction and magnitude of the phase shift for f(x) = sin(x + π 6) − 2.
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Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Graph Cheat Sheet | Desmos
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The first transformation we'll look at is a vertical shift. Given the graph of f (x) f ( x) the graph of g(x) = f (x) +c g ( x) = f ( x) + c will be the graph of f (x) f ( x) shifted up by c c units if c c is positive and or down by c c units if c c is negative. So, if we can graph f (x) f ( x) getting the graph of g(x) g ( x) is fairly easy.
Andreas Grech's Blog A Function Transformations reference sheet
Sheet What really is a function? Before we can properly define a function, we must first understand mappings. A A mapping takes a set of numbers = 2 and transforms them into another set of numbers. Mappings are often represented by algebraic equations.
