Transformation Calculator

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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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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Homeschool Math. Squeezing & Stretching. There are two other transformations, but they're harder to "see" with any degree of accuracy. 2 ×½ ×) = (½) (This is skinnier than the regular function's graph, in the box below.) (This is the graph of the regular function.) (This is fatter than the graph of the regular function, which was shown in.

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A one-page cheat sheet on Graph Transformations, covering summarized theory and the most important formulas. Free Download (PDF)

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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.

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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.

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Summary of Transformations . March 2017 MVCC Learning Commons Math Lab . Graph Draw the graph of f(x) and: Changes in f(x). Shift the graph f(x) to the left c units -subtract c from x coordinate . Shift the graph f(x) to the right c units -add c to x coordinate . Reflection about the x-axis ;

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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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Function Transformations When studying the transformations that can occur in the graph of a function, we have as objective to develop the perception that the knowledge of the graph of a very simple function, will allow us to discover the graphs of other functions, which being of the same type, result from the one of these transformations.

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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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Translations are a slide or shift. Translations can be achieved by performing two composite reflections over parallel lines. Translations are isometric, and preserve orientation. Coordinate plane rules: (x, y) (x ± h, y ± k) where h and k are the horizontal and vertical shifts. Note: If movement is left, then h is negative.

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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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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.

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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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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