algebra 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 2Graph Transformations There are many times when you'll know very well what the graph of a particular function looks like, and you'll want to know what the graph of a • Beginning with the graph f(x)=x2, we can use the chart on the previous page to draw the graphs of f(x 2),f(x 2), f(2x), f(1 2x), and f(x)Graph of will occur A horizontal shrinking pushes the graph of toward the yaxis In general, a horizontal stretching or shrinking means that every point (x, y) on the graph of is transformed to (x/c, y) on the graph of 𝑓𝑥 𝑥2 v 𝑓 𝑥 2 v 𝑥 3 𝑥 u2 𝑓 𝑥 𝑥 𝑓 𝑥 u 𝑥 u 𝑓 t𝑥 t𝑥
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Graph of y=x^2 transformations-Watch Video in App Continue on Whatsapp This browser does not support the video element 652 k 33 k Answer\(y = (x a)^2\) 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
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All right So today we're graphing transformations and we're graphing transformations of the parent function y equals X squared So just a quick reminder We know that the graph of y equals X squared Just a basic proble like that Not exactly like that But you get the idea for party were given g of X equals X squared plus one So looking at this graph right here, we can make some(1 point) A translate 2 units to the left, translate down 2 units, stretch by the 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 D reflect across the xaxis, translate 2 The general form for a sine function isy = A*sin(B(xC)) Dwhere,A = amplitudeB = 2pi/T, with T being the period, so T = 2pi/BC = phase shiftD = midlinePut a meredith meredith Mathematics High School answered How do transformations affect the graph of y = sin (x) and y= cos(x)?
Here 1 is subtracted from x, so we have to shift the graph of y = x 2, 1 unit to the right side Step 3 The positive number 3 is multiplied by (x1) which is greater than 1, so we have to compress the curve y = (x1) 2 towards yaxisLet us start with a function, in this case it is f(x) = x 2, but it could be anything f(x) = x 2 Here are some simple things we can do to move or scale it on the graph We can move it up or down by adding a constant to the yvalue g(x) = x 2 C Note to move the line down, we use a negative value for C C > 0 moves it up;We're told the graph of the function f of X is equal to x squared we see it right over here in gray is shown in the grid below graph the function G of X is equal to X minus 2 squared minus 4 in the interactive graph and this is from the shifting functions exercise on Khan Academy and we can see we can change we can change the we can change the graph of G of X but let's see we want to graph
C < 0 moves it down We can move it left or right by adding a constant to the xvalue g(x) = (xC) 2 So, for any given yvalue, the xvalue that gets you there is moved 5 units to the negative side of the graph, which is left These two simple transformations up and down shift the asymptotes of23 Transformations of Graphs 81 There are some importantobservations we must make in looking at the horizontal shifts in Example 2 While the graph of y 5 x2 2 2 shifts down from the graph of y 5 x2,thegraphofy5~x22!2is shifted to the right,the opposite direction from what some people expect It may help to remember that the
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Solution I Have A Question That States A Use The Transformations On The Graph Of Y X 2 To Determine The Graph Of Y X 5 2 9 B Using The Graph Of F X X 2 As A Guide Graph
Answer (1 of 6) > Shift the graph f the parabola y=x^2 by 3 units to the left then reflect the graph obtained on the xaxis and then shift it 4 units up What is theY = f (x) = 1/x = x^1 which I think would help to be written in this form 3/x = 3x^1 so you can see that the transformation affects the the function and not 'x' If f (x) = 1/x then 3 f (x) = 3 (1/x) = 3/x as required Another way I like to think about it, for translations and reflections, think about the f (x) = x^2 graph and forFree functions and graphing calculator analyze and graph line equations and functions stepbystep This website uses cookies to ensure you get the best experience By using this website, you agree to our Cookie Policy
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About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How works Test new features Press Copyright Contact us CreatorsThe graph of \(f(x) = x^2\) is the same as the graph of \(y = x^2\) Writing graphs as functions in the form \(f(x)\) is useful when applying translations and reflections to graphs TranslationsTransformation of graph y = {f({x})} Updated On 30 To keep watching this video solution for FREE, Download our App Join the 2 Crores Student community now!
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Transformations of Quadratic Functions Learning Outcomes The standard form is useful for determining how the graph is transformed from the graph of latexy={x}^{2}/latex The figure below is the graph of this basic function Shift Up andNote When using the mapping rule to graph functions using transformations you should be able to graph the parent function and list the "main" points Example 3 Use transformations to graph the following functions a) h(x) = −3 (x 5)2 – 4 b) g(x) = 2 cos (−x 90°) 8 Solutions a) The parent function is f(x) = x2The x1 indicate to shift to the right one unit Again it's counter intuitive The x1 you might think shifts the graph to the left but it shifts it to the right So let's just review really quickly what this transformation does y equals half of x xh is a horizontal shift If each is positive it shifts the graph to the right Like when h was
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View my channel http//wwwyoutubecom/jayates79View Sec 26 Graphs and Transformationsdocx from MATH 1314 at Collin College Section 26 – Basic Functions and Their Graphs Vertical and Horizontal Shifts If y=f (x) is a function, then theDescribe the transformations necessary to transform the graph of f(x) (solid line) into that of g(x) (dashed line) 1) x y reflect across the xaxis translate left units 2) x y compress vertically by a factor of translate up units Describe the transformations necessary to transform the graph of f(x) into that of g(x) 3) f (x) x
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In order to graph the function {eq}f(x)=(x2)^2 {/eq}, we need to translate the graph of the parent function by 2 units to the left Note that adding a units in the xvariable means translatingTransformations to the graph of y = x^2 Move the sliders 'a' 'h' and 'k' to explore the transformations applied to the graph of y=x^2 Notice the green dotted line is the Axis of Symmetry, where x = hWhich steps transform the graph of y = x2 to y = –2(x – 2)2 2?
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This modified versions of the basic graph are graphical transformation To start, let's consider the quadratic function y=x2 Its basic shape is the redcoloured graph as shown Furthermore, notice that there are three similar graphs (bluecoloured) that are transformations of the original g (x)= (x5)2 Horizontal translation by 5 units toGraph 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 graphs are translated, or moved about the x yThe parent function is the simplest form of the type of function given y = x2 y = x 2 For a better explanation, assume that y = x2 y = x 2 is f (x) = x2 f ( x) = x 2 and y = −x2 4 y = x 2 4 is g(x) = −x2 4 g ( x) = x 2 4 f (x) = x2 f ( x) = x 2 g(x) = −x2 4 g ( x) = x 2 4
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Therefore the graph should look like the following graph {y= (2x)^2 10, 10, 5, 5} To describe the transformation of the graph, follow RST (Reflection, Stretch/Compression, Translation) The description would be the following The parabola is stretched by a factor of 4The answer is either Translation 2 units to the left, then reflect across the axis, or reflect across the axis, then translate 2 units to the right Note that both of the transformations are horizontal changes — that is, they arise from things that we do toA 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 If we add a positive constant to each ycoordinate, the graph will shift up If we add a negative constant, the graph will shift down
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Transformations Transformations are the key to graphing and explaining where the parabola is It is only used in vertex form because each letter except x and y represents a transformation in this equation y=a (xh)^2k h = the vertex of the parabola will move to the right or left side of the graph (Negative numbers move right and positiveGraphing Quadratic Equations Using Transformations A quadratic equation is a polynomial equation of degree 2 The standard form of a quadratic equation is 0 = a x 2 b x c where a, b and c are all real numbers and a ≠ 0 If we replace 0 with y , then we get a quadratic function y = a x 2 b x c whose graph will be a parabolaIn this section we will discuss the transformations of the three basic trigonometric functions, sine, cosine and tangent Note You should be familiar with the sketching the graphs of sine, cosine You should know the features of each graph like amplitude, period, x –intercepts, minimums and maximums The information in this section will be inaccessible if your proficiency with those
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Transformations of Graphs (a, h, k) Consider the function y = f (x) We're going to refer to this function as the PARENT FUNCTION The following applet allows you to select one of 4 parent functions The basic quadratic function f (x) = x^2 The basic cubic function f (x) = x^3 The basic absolute value function f (x) = x The basic squareTransformations of Quadratic Functions / Instruction STUDY Flashcards Learn Write Spell Test PLAY Match Gravity Created by Ryman6969 Terms in this set (9) The graph of g(x) = x2 2 is a translation of the graph of f(x) updownleftright by units up, 2 / down, 3 The graph of g(x) = (x 2)2 is a translation of the graph of f(x) X upThe graph of y = f(x) c is the graph of y = f(x) shifted c units vertically upwards The graph of y = f(x) c is the graph of y = f(x) shifted c units vertically downwards g(x) = x2 2 = f(x) 2 h(x) = x2 – 3 = f(x) – 3 Look for the positive and negative sign Positive sign makes the graph
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Remove parentheses y = 2 x y = 2 x y = 2x y = 2 x The transformation from the first equation to the second one can be found by finding a a, h h, and k k for each equation y = abx−h k y = a b x h k Find a a, h h, and k k for f (x) = 2x f ( x) = 2 x a = 1 a = 1 h = 0 h = 0 k = 0 k = 0Y = 3(x −2)2 1 y = 3 ( x 2) 2 1 The horizontal shift depends on the value of h h The horizontal shift is described as g(x) = f (xh) g ( x) = f ( x h) The graph is shifted to the left h h units g(x) = f (x−h) g ( x) = f ( x h) The graph is shifted to the right h h units To begin graphing, we can start with graphing the parent function (that is #y=x^2#) first and work our way up from there graph{x^2 10, 10, 2, 5} If we recall our transformation rules, we would know that the graph #y=(x4)^2# means that we shift the entire function #color(red) 4# units to the #color(red)("right")# So our final function looks like this graph{(x
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