Given the function f(x)= is reflected across the xaxis to create g(x) The rule of reflection across x axis is then;The graph of g(x) = ()x is the graph of f(x) = 2x reflected over the yaxis Which graph represents g(x)?Reflecting Over the xaxis Another effect of " a " is to reflect the graph across the x axis When the parent function f (x) = x2 has an a value that is less than 0, the graph reflects across the x axis before it is transformed The graph below represents the function f (x) = x2 In function notation, this reflection is represented by a
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Which graph shows f(x) = x 2 reflected over the x-axis
Which graph shows f(x) = x 2 reflected over the x-axis-Let y = f(x) be a function In the above function, if we want to do reflection through the yaxis, x has to be replaced by x and we get the new function y = f(x) The graph of y = f(x) can be obtained by reflecting the graph of y = f(x) through the yaxisThe graph of the function f(x)=log6(x) is stretched vertically by a factor of 3, reflected over the xaxis, reflected over the yaxis, and shifted up by 4 units Find the equation of the function g(x) described above
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B 2/3 Chelsea is graphing the function f(x) = ()xFirst image A Which function represents g(x), a reflection of If f (x) Makes you reflect over the x axis Then e^x will do a neccesary reflection for reflecting it about y = 2 Then I add 2 to the end of f (x) = (e^x)2 = 2e^x Although on my homework they say the correct answer is 4 e^x Saying I needed to time 2 for some reason, which is where I lose understanding
And y=f (x) is a reflection across the yaxis because the negative is in the second term of the right hand side of the equation (x) and because the second coordinate we plot in a graph is the Ycoordinate and y=f (x) that's easy to remember because both are negative and you just reflect the function in both axisThe axis of symmetry is simply the vertical line that we are performing the reflection across It can be the yaxis, or any vertical line with the equation x = constant, like x = 2, x = 16, etc Finding the axis of symmetry, like plotting the reflections themselves, is also a simple processOr therefore, the function g(x) = Since, this g(x) is an exponential function it is of the form of where a is the initial value On comparing we get ;
Functions of graphs can be transformed to show shifts and reflections Graphic designers and 3D modellers use transformations of graphs to design objects and imagesB The table represents an exponential function What is the multiplicative rate of change of the function?Can someone help Nothing, Jose, nothing changes y = x 2 is symmetric with respect to the yaxis Plug in numbers and try it out The negative of all your numbers should give you the same result as the positive ones
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G(x) = 2/5 (10)x The function g(x) = 8(4x) is reflected across the xaxis to create f(x) What is the equation for f(x)?8 Which graph represents a reflection of f(x) = 2(04)x across the yaxis?Graph functions using reflections about the xaxis and the yaxis Another transformation that can be applied to a function is a reflection over the x – or y axis A vertical reflection reflects a graph vertically across the x axis, while a horizontal reflection reflects a graph horizontally across the y axis If the graph #y=x^3 5# is reflected in the x axis what is the new equation?
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G(x) is shifted 2 units to the right and reflected over the xaxis g(x) is shifted 2 units to the left and reflected over the xaxis g(x) is shifted 2 units to the right and 1 unit up g(x) is shifted 2 units to the right and 1 unit downReflect {eq}f(x) = x^2 {/eq} about the {eq}y {/eq}axis Relection across the yaxis When we are reflecting a function over the yaxis, what happens is that the points on the right side of the y The graph of g(x) is the graph of f(x) reflected over the xaxis, translated 6 units to the left and shifted down 3 units Write the equation for g(x) Algebra 2 the function f(x)=5x The graph of g(x) is f(x) vertically compressed by a factor of 1/4 and reflected in the x axis What is the function rule for g(x)
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Reflect over xaxis Down 2 Reflect over yaxis Up 2 Reflect over xaxis Up 2 Reflect over yaxis Down 2 s Question 11 SURVEY 30 seconds Report an issue Q g(x)=f(x)4 Describe the transformation to f(x) that results in g(x) answer choices f(x) has been translated down 4 f(x) has been translated up 4D To reflect a graph over the line y = x, switch the x and y coordinates of each point on the graph For this graph, Point V (2,1) becomes (1,2) and point Z (0,1) becomes (1,0) Eliminate any graph that does not include these three points Note that point X (1,1) remains the same"A reflection through the x axis" And also write the formula that gives the requested transformation and draw the graph of both the given function and the transformed function Answer Step 1 Since we do reflection transformation through the xaxis, we have to replace y by y in the given function y = √x Step 2 So, the formula that gives the requested transformation is y = √x
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Which function represents g(x), a reflection of f(x) = 2/5 (10)x across the xaxis? Correct answers 1 question How does the graph of g(x) = −(x − 2)4 compare to the parent function of f(x) = x4? To reflect a graph, f(x) over the xaxis, you take f(x) So if f(x)=x^2, then f(x) is x^2 Then g(x)=x^2 is the reflection of your function f(x) over the xaxis
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Reflect f(x)=x^2 about the yaxis What changes?I am going to do it in the order yo gave (1) Reflect about xaxis This means let y > y (or take the negative of the function) y=(x3)^2 5 goes to y=(x3)^2 5 or y= (x3)^2 5 I moved the minus sign over in the last step (2) HorizontTransform the function f(x) as described and write the resulting function as an equation f(x)=x^2 Translate left 2 units stretch horizontally by a factor of 2 reflect over the xaxis stretch vertically by a factor of 3 translate up 4 units Start with the red graph Translate left 2 units replace x by (x2) the green graph
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What you'll find in this video1) What are reflections?Reflected over the xaxis, vertical stretch, and shifted right 5 Reflected over the xaxis, vertical stretch, and shifted left 5 Shifted right 5, shifted down 2 s Question 3 SURVEY 60 seconds Q What are the transformations to the graph compared to the parent function y=√(x)?How does the graph of g (x) = (x 2) 4 compare to the parent function of f (x) = x4?
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Solution Step 1 Place a negative sign in front of the righthand side of the function f(x) = x 2 – 3 becomes g(x) = – (x 2 – 3) Step 2 Remove the parentheses, carrying through the negative sign g(x) = x 2 3Vertically stretching mathf(x)=x^2/math by 7 gives mathf(x)=7x^2/math Moving it down 5 means dropping the y value, or f(x) by 5, so we now have math7x^2–5/math Reflecting over the x axis means you want your y values to become the oppStep 1 Know that we're reflecting across the xaxis Since we were asked to plot the – f (x) f(x) f (x) reflection, is it very important that you recognize this means we are being asked to plot the reflection over the xaxis When drawing reflections across the x x x and y y y axis, it is very easy to get confused by some of the notations So, make sure you take a moment before solving any
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(018)2) Reflection over xaxis(036)3) Rigid Motion (214)4) Reflection over yaxis (1)5) ReflectThe functions f(x) and g(x) are reflections over the yaxis the function f(x) is a decreasing function, and g(x) is an increasing function the function f(x) has a greater initial value than g(x) ja niin14 Answers 2 Get Other questions on the subject MathematicsPrecalculus Functions Defined and Notation Introduction to Twelve Basic Functions 2 Answers Gerardina C #y=x^35# Explanation the points reflected in the x axis have opposite ycoordinates, or x'=x and y'=y
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D An exponential function f(x) is reflected across the yaxis to create function g(x) Which is a true statement regarding f(x) and g(x)? It means the y coordinate is same and the sign x coordinate changed So, the equation of given graph after reflection across the y axis is, After reflection the graph shifts 2 unit down If a graph translate 2 unit down then, So, the function f (x) is, Therefore the equation of f (x) is search rotate When a function f(x) is reflected over the xaxis, it becomes a new function g(x) = – f (x) Example Question #2 What is f(x) = x 2 – 3 reflected over the xaxis?
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For example, when point P with coordinates (5,4) is reflecting across the Y axis and mapped onto point P', the coordinates of P' are (5,4)Notice that the ycoordinate for both points did not change, but the value of the xcoordinate changed from 5 to 5 You can think of reflections as a flip over a designated line of reflectionMore Like other functions, f (x) = a g (bx), if a is negative (outside) it reflects across x axis and if b is negative it reflects across the y axis So for square root functions, it would look like y = a √ (bx) Outside reflect across x such as y = √x, and inside reflect across y such as y = √xThe 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 = a√x− hk y = a x h k Factor a 1 1 out of the absolute value to make the coefficient of x x equal to 1 1 y = √x y = x Find a a, h h, and k k for y = √x y = x a = 1 a = 1
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This video explains to graph graph reflections across the xaxis and yaxis in the form a*f(b(xc))d This video looks at how the sign of a and b affect thUsing the rule of reflection across xaxis;The initial value of g(x) is 2 Now, to find the output for inputs of 1 and 1 in g(x);
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From the diagram we see the object point ( − 2, −5) is mapped to (x',y') by a reflection in the line X = 2 we note (1) the ycoordinate is unaffected (2) for reflections the distance from the line of reflection to the object is equal to the distance to the image point ∴ a = 2 2 = 4units so the image point is 4 units from the line ofSo it's originally, uh, negative X and that is going to be changed to a positive X And that's how we will reflect about the Y axis and then to vertically compress the function by 1/5 We simply multiply the function by one, fits will have won this times 1/2 to the X because we are reflecting about the y axis This goes back to our first step1 The equation for the transformed function is f(x) = ( −x − 6)3 4 2 a) The parent function is f(x) = x2 The parent function has been reflected in the xaxis, vertically stretched by a factor of 3, translated 8 units to the left and 5 units down b) The parent function is g(x) = √
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The reflected image has the same size as the original figure, but with a reverse orientation Examples of transformation geometry in the coordinate plane Reflection over y axis (x, y) ( x , y )The graph of f(x) = x is reflected over the yaxis and horizontally stretched by a factor of 3 8(x) = a The graph of f(x) = r is vertically compressed by a factor of then shifted to the left 9 units and up 4 units 3 8(x) = b The graph of f(x) = x2 is horizontally stretched by a factor of 6, then shifted to the left 2 units and down 9 unitsDescribe the Transformation f(x)=(x1)^22 The parent function is the simplest form of the type of function given Reflection about the xaxis Reflected The graph is reflected about the yaxis when Reflection about the yaxis None Compressing and stretching depends on the value of
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The function f(x) = 011(3)x is reflected over the xaxis to produce function g(x) Function g(x) is then reflected over the yaxis to produce function h(x) Which function represents h(x)?Graphing Reflections In addition to shifting, compressing, and stretching a graph, we can also reflect it about the xaxis or the yaxisWhen we multiply the parent function latexf\left(x\right)={b}^{x}/latex by –1, we get a reflection about the xaxisWhen we multiply the input by –1, we get a reflection about the yaxisFor example, if we begin by graphing the parent 👍 Correct answer to the question If f(x)=x^2 is vertically stretched by a factor of 4 to g(x) and reflected over the xaxis, what is the equation for g(x)?
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A) g (x) is shifted 2 units to the right and reflected over the xaxis b) g (x) is shifted 2 units to the left and reflected over the xaxis c) g (x) is shifted 2 units to the right and 1 unit up d) g (x) is shifted 2 units to the right and 1 unit down
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