Algebra Describe the Transformation y=x^2 , y=3x^2 y = x2 y = x 2 , y = 3x2 y = 3 x 2 For a better explanation, assume that y = x2 y = x 2 is f (x) = x2 f ( x) = x 2 and y = 3x2 y = 3 x 2 is g(x) = 3x2 g ( x) = 3 x 2 f (x) = x2 f ( x) = x 2 g(x) = 3x2 g ( x) = 3 x 2 Which steps transform the graph of y=x^2 to y=2 (x2)^22 a) translate 2 units to the left translate down 2 units stretch by factor 2 b)translate 2 units to the right translate up 2 units stretch by the factor 2 c)reflect across the xaxis translate 2A nonrigid transformation A set of operations that change the size and/or shape of a graph in a coordinate plane changes the size and/or shape of the graph A vertical translation A rigid transformation that shifts a graph up or down is a rigid transformation that shifts a graph up or down relative to the original graph This occurs when a constant is added to any function
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Graph of y=x^2 transformations-Graph Of Y X 2 Transformations ihličnaté stromy v kvetináči hviezda v súhvezdí orol inovovaný štátny vzdelávací program isced 1 hugolín gavlovič valaská škola if f x x 4 2x 3 3x 2 ax b informovaný súhlas rodiča výlet vzor ii rákóczi ferenc gimnázium budapest incheba vianocne trhy 19 impresia východ slnka hviezdoslavov 17 Transformations In this section, we study how the graphs of functions change, or transform, when certain specialized modifications are made to their formulas The transformations we will study fall into three broad categories shifts, reflections and scalings, and we will present them in that order
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Graphing Transformations Use the graph of y=x^{2} in Figure 4 to graph the following \begin{array}{ll}{\text { (a) } g(x)=x^{2}1} & {\text { (b) } g(x)=(x1)FUNCTION TRANSFORMATIONS WORKSHEET Problem 1 Submit an equation that will move the graph of the function y = x2 right 4 units Problem 2 The equation y = (x 3)2 – 2 moves the parent function y = x2 right 3 units and down 2 units Problem 3 Submit an equation that will move the graph of the function y = x2 down 7 unitsThe graph of this function changes to y = −x2 y = − x 2 The graph transformation that happens in this function is Reflection over the xaxis Reflection over the xaxis
VCE Maths Methods Unit 3 Transformation of functions Finding equations from transformation (graphs) 10 • The equations of transformed functions can be found from graphs • For every unknown constant, one piece of information will be required to help to "nd them • Points, stationary points and asymptotes are used y= a (x−h)2 k x=3 When the graph of a function is changed in appearance and/or location we call it a transformation There are two types of transformations A rigid transformation 57 changes the location of the function in a coordinate plane, but leaves the size and shape of the graph unchanged A nonrigid transformation 58 changes the size and/or shape of the graphGraphs and Transformations wwwnaikermathscom Graphs and Transformations Edexcel Past Exam Questions 2 1 Figure 1 Figure 1 shows a sketch of the curve C with equation y = f(x), where f(x) = x2(9 – 2x)There is a minimum at the origin, a maximum at the point (3, 27) and C cuts the xaxis at the point A (a) Write down the coordinates of the point A
23 Transformations of Graphs 79 happens for each kind of transformation we examine Accordingly, we will show lots of graphs, but for your benefit, we strongly encourage you to use your graphing y =(x–2)2 (a) Right 2 units (1, 0) y x y = x2 –21 = (x –1)2 (c) Right 1 unit pg080 V G2 / HCG / Cannon & Elich jb MP3The graphs of these functions are drawn on the next page Notice on the next page that the graph of (x)2 is the same as the graph of our original function x 2 That's because when you flip the graph of x over the yaxis, you'll get the same graph that you started with That x2 and ( 2x) have the same graph means that they are the same function We know We are asked to find the two transformations that can be used to obtain the transformed function We will use transformation rules to solve our given problem, where a is any positive number We can see that the value of a is 5 for our given function, therefore, graph is shifted to right by 5 units Now we will use scaling rules
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From the parent function y = x 2, if it is moved 7 units to the left, we will have the function y = (x 7) 2 Further, if it is moved 3 units down, the function will be y = (x 7) 2 3 Problem 2 Which equation will shift the graph of y = x 2 up 9 units ?New Blank Graph Examples Lines Slope Intercept Form example Lines Point Slope Form example Lines Two Point Form example Parabolas Standard Form example Parabolas Vertex Form👍 Correct answer to the question The coordinates of the turning point of the graph of y = x 2 − 8x 25 is (4,9) Hence describe the single transformation which maps the graph of y = x 2 onto the graph of y = x 2 − 8x 25 eeduanswerscom
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\(y = (x a)^2\) represents a translation parallel to the \(x\)axis of the graph of \(y = x^2\) If \(a\) is positive then the graph will translate to the left If the value of \(a\) is negative Which steps transform the graph of y=x^2 to y=2(x2)^22 a) translate 2 units to the left translate down 2 units stretch by factor 2 b)translate 2 units to the right translate up 2 units stretch by the factor 2 c)reflect across conics The graph of y=x^2 is reflected in the xaxis, then stretched vertically by a factor of 2, and then Which steps transform the graph of y=x^2 to y=2 (x2)^22 a) translate 2 units to the left translate down 2 units stretch by factor 2 b)translate 2 units to the right translate up 2 units stretch by the factor 2 c)reflect across the xaxis translate 2 units to the left translate down 2 units stretch by the factor 2
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The parent function of the graph is y=x^2 Using the general equation y=af(kxd)c, Where if a > 1=vertical stretch, 0< a < 1= vertical compression f(x)=reflection in the xaxis f(x)=reflection in the yaxis 0 < k < 1= horizontal stretch, k > 1= horizontal compression d=horizontal shift to the right d= horizontal shift to the left c= vertical translation upwardsGraph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph It's a common type of problem in algebra, specifically the modification of algebraic equations Sometimes graphsMathematics Revision Guides – Transformations of Graphs Page 3 of 9 Author Mark Kudlowski The xtranslation This example will take the function y=x3 and transform it into y = (x 2)3 and y = (x 1)3 x selected y = x3 selected y = (x 2) 3 selected y = (x 1) 35 27
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Y=X^2 Transformations Y=X^2 Transformations $$ ≥ $$ 1 $$ 2 $$ 3 $$ − A B C $$ $$ π $$ 0 $$ $$ = $$ Sign UporLog In to save your graphs!3) Describe, using transformations how the graph of y=x^2 can be transformed into the graph of the quadratic relation (16 marks) a) y= 5x^24 c) y = 1/4 (x5)^2 b) y=3 (x2)^27 d) T (x,y) → (x2,5y3) 4) List the features of this parabola and the step pattern (5 marks) y = 2x² 4x5 vGraph exponential functions using transformations Transformations of exponential graphs behave similarly to those of other functions Just as with other parent functions, we can apply the four types of transformations—shifts, reflections, stretches, and compressions—to the parent function f ( x) = b x \displaystyle f\left (x\right)= {b
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