Graphing Reflections 1
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Question 1 of 8
1. Question
Given f(x)=x2-4x
Sketch y=-f(x).
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Reflections around the x-axis have the property y=-f(x)Replace yโ-y.To sketch the transformed function y=-f(x), start by sketching the original function f(x)=x2-4x.Find the points where the graph of f(x)=x2-4x crosses the x-axis.0= x2-4x Set y=0 to find the points where the graph crosses the x-axis. 0= x(x-4) Factor out x from both terms. Solve x=0.x= 0 y= (0)2-4(0) When x=0, solve for y. y= 0 A(0,0) Solve x-4=0.x-4= 0 x= 4 y= (4)2-4(4) When x=4, solve for y. y= 16-16 y= 0 B(4,0) Find the vertex. Take the two x values and find the halfway point (4+02=2).y= (2)2-4(2) Find the y value when x=2. y= 4-8 y= -4 Vertex 1(2,-4) Sketch the original function f(x)=x2-4x by using the points Vertex(2,-4), A(0,0) and B(4,0). Remember that this function is a concave up parabola (positive x2 function).Now sketch the transformed function y=-f(x) which is f(x)=-(x2-4x)=-x2+4x.Find the points where the graph of f(x)=-x2+4x crosses the x-axis.0= -x2+4x Set y=0 to find the points where the graph crosses the x-axis. 0= -x(x-4) Factor out a -x from both terms. Solve -x=0.-x= 0 x= 0 y= (0)2-4(0) When x=0, solve for y. y= 0 C(0,0) Solve x-4=0.x-4= 0 x= 4 y= (4)2-4(4) When x=4, solve for y. y= 16-16 y= 0 D(4,0) Find the vertex. Take the two x values and find the halfway point (4+02=2).y= -(2)2+4(2) Find the y value when x=2. y= -4+8 y= 4 Vertex 2(2,4) Sketch the transformed function f(x)=-x2+4x by using the points Vertex 2(2,4), C(0,0) and D(4,0). Remember that this function is a concave down parabola (negativex2 function). -
Question 2 of 8
2. Question
Graph y=(x-3)2 reflected in the x-axis.
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Reflections around the x-axis have the property y=-f(x)Replace yโ-y.To sketch the reflected function, take y=(x-3)2 and then replace y for -y and you will get: y=-(x-3)2.Use a table of values to sketch y=(x-3)2 and y=-(x-3)2.x 1 2 3 4 5 (x-3)2 4 1 0 1 4 -(x-3)2 -4 -1 0 -1 -4 Sketch the graph of y=(x-3)2 and y=-(x-3)2 using the table of values. -
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Question 3 of 8
3. Question
Graph y=2x reflected in the y-axis.
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Reflections around the y-axis have the property y=f(-x)Replace xโ-x.To sketch the reflected function, take y=2x and then
replace x for -x and you will get: y=2-x.Use a table of values to sketch y=2x and y=2-x.x -3 -2 -1 0 1 2 3 2x 18 14 12 1 2 4 8 2-x 8 4 2 1 12 14 18 Sketch the graph of y=2x and y=2-x using the table of values. -
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Question 4 of 8
4. Question
Graph y=(x-1)2 reflected in the y-axis.
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Chapters- Chapters
Reflections around the y-axis have the property y=f(-x)Replace xโ-x.To sketch the reflected function, take y=(x-1)2 and then replace x for -x and you will get: y=(-x-1)2.Use a table of values to sketch y=(x-1)2 and y=(-x-1)2 which can also be written as:y=(-1)2 (-x-1)2โy=(x+1)2x -2 -1 0 1 2 3 (x-1)2 9 4 1 0 1 4 (x+1)2 1 0 1 4 9 16 Sketch the graph of y=(x-1)2 and y=(x+1)2 using the table of values. -
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Question 5 of 8
5. Question
Graph y=โx reflected in the x-axis.
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Chapters- Chapters
Reflections around the x-axis have the property y=-f(x)Replace yโ-y.To sketch the reflected function, take y=โx and then
replace y for -y and you will get: y=-โx.Use a table of values to sketch y=โx and y=-โx.x 0 1 2 3 4 5 โx 0 1 1.4 1.7 2 2.2 -โx 0 -1 -1.4 -1.7 -2 -2.2 Sketch the graph of y=โx and y=-โx using the table of values. -
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Question 6 of 8
6. Question
Given f(x)=x3
Sketch y=-f(x)
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Chapters- Chapters
Reflections around the x-axis have the property y=-f(x)Replace yโ-y.To sketch the reflected function, take y=x3 and then
replace y for -y and you will get: y=-x3Use a table of values to sketch y=x3 and y=-x3x -2 -1 0 1 2 x3 -8 -1 0 1 8 -x3 8 1 0 -1 -8 Sketch the graph of y=x3 and y=-x3 using the table of values. -
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Question 7 of 8
7. Question
Given f(x)=x3+1.
Sketch y=f(-x)
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Chapters- Chapters
Reflections around the y-axis have the property y=f(-x)Replace xโ-x.To sketch the transformed function y=f(-x), start by sketching the original function f(x)=x3+1.Find the points where the graph of f(x)=x3+1 crosses the y-axis.Solve x=0.x= 0 y= (0)3+1 When x=0, solve for y. y= 1 A(0,1) Solve x3+1=0.x3+1= 0 x= -1 y= (-1)3+1 When x=-1, solve for y. y= -1+1 y= 0 B(-1,0) Sketch the original function f(x)=x3+1 by using the pointsA(0,1) and B(-1,0). Remember that this function is a cubic function (positive x3 function).Now sketch the transformed function y=f(-x) which is f(-x)=(-x)3+1=-x3+1.Find the points where the graph of f(-x)=-x3+1 crosses the y-axis.Solve -x=0.-x= 0 x= 0 y= (0)3+1 When x=0, solve for y. y= 1 C(0,1) Solve -x3+1=0.-x3+1= 0 x= 1 y= -(1)3+1 When x=1, solve for y. y= -1+1 y= 0 D(1,0) Sketch the transformed function f(-x)=-x3+1 by using the points C(0,1) and D(1,0). Remember that this is a negative cubic function. -
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Question 8 of 8
8. Question
Given f(x)=x2+4x.
Sketch y=f(-x)
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Great Work!
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Subtitles- subtitles off
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- English
Chapters- Chapters
Reflections around the y-axis have the property y=f(-x).Replace xโ-x.To sketch the transformed function y=f(-x), start by sketching the original function f(x)=x2+4x.Find the points where the graph of f(x)=x2+4x crosses the y-axis.0= x2+4x Set y=0 to find the points where the graph crosses the x-axis. 0= x(x+4) Factor out an x from both terms. Solve x=0.x= 0 y= (0)2+4(0) When x=0, solve for y. y= 0 A(0,0) Solve x+4=0.x+4= 0 x= -4 y= (-4)2+4(-4) When x=-4, solve for y. y= 16-16 y= 0 B(-4,0) Find the vertex. Take the two x values and find the halfway point (-4+02=-2).y= (-2)2+4(-2) Find the y value when x=-2. y= 4-8 y= -4 Vertex 1(-2,-4) Sketch the original function f(x)=x2+4x by using the points Vertex(-2,-4), A(0,0) and B(-4,0). Remember that this function is a concave up parabola (positive x2 function).Now sketch the transformed function y=f(-x) which is f(-x)=(-x)2+4(-x)=x2-4x.Find the points where the graph of f(-x)=x2-4x crosses the x-axis.0= x2-4x Set y=0 to find the points where the graph crosses the x-axis. 0= x(x-4) Factor out an x from both terms. Solve x=0.x= 0 y= (0)2-4(0) When x=0, solve for y. y= 0 C(0,0) Solve x-4=0.x-4= 0 x= 4 y= (4)2-4(4) When x=4, solve for y. y= 16-16 y= 0 D(4,0) Find the vertex. Take the two x values and find the halfway point (4+02=2).y= (2)2-4(2) Find the y value when x=2. y= 4-8 y= -4 Vertex 2(2,-4) Sketch the transformed function f(-x)=x2-4x by using the points Vertex 2 (2,-4), C(0,0) and D(4,0). Remember that this function is a concave up parabola (positive x2 function). -
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Quizzes
- Vertical Translations 1
- Vertical Translations 2
- Vertical Translations from a Point
- Horizontal Translations 1
- Horizontal Translations 2
- Horizontal Translations from a Point
- Horizontal Translations from a Graph
- Horizontal and Vertical Translations from a Graph
- Sketch a Graph using Translations
- Write the Equation from a Graph
- Write the Equation from Translations
- Vertical Dilations
- Horizontal Dilations 1
- Horizontal Dilations 2
- Horizontal Dilations โ Scale Factor
- Horizontal and Vertical Dilations 1
- Horizontal and Vertical Dilations 2
- Horizontal and Vertical Dilations 3
- Graphing Reflections 1
- Graphing Reflections 2
- Reflection with Rotation
- Combinations of Transformations: Order
- Combinations of Transformations: Coordinates
- Combinations of Transformations: Find Equation 1
- Combinations of Transformations: Find Equation 2
- Combinations of Transformations: Find Equation 3