Copy of Linear Relations Transformations

Linear Relations Transformations

Linear Relation Transformation Exercise

[br][b][size=150]The linear Relation [color=#6aa84f]y = x[/color], denoted by line g. [br][/size] [br][/b]The slope-intercept form is[b][color=#ff0000]y = mx + b[/color][/b], where m=slope and b=y-intercept of the relation.[br][br][size=150][color=#ff0000][b]Note[/b][/color][/size]: The 'slider' feature on the x-y coordinate plane can be used to change the [color=#ff0000][b]m and b[/b][/color] along with a new parameter [b][color=#ff0000]c [/color][/b]for the following exercises. To do so, place the cursor and hold it on the dot of the slider and slide it to the desired m and b values. To move the slider to a different location on the x-y plane, place the cursor and hold it on the line of the slider and move it to the desired location.[br][br][b] Note: You can zoom in or out with the mouse.[/b]

Exercise 1

[size=150][b]Perform the following linear relation transformation:[br][/b][/size][br][b]Vertical shift of 3 units up (y-intercept = 3). [br][br][/b] [color=#0000ff]The new relation is [/color][b][color=#ff0000]y=x +3[/color][/b][color=#0000ff] , denoted by line f.[br] Set the slope of the relation to m=1 by entering 1 for m.[br] Set the y-intercept of the relation to b=3 by entering 3 for b. [br] Set the x-intercept of the relation to c=0 by entering 0 for c. [br][/color][b] Observe the transformation of the linear relation.[/b]

Exercise 2

[b]Perform the following linear relation transformation:[br][/b][br][b]Vertical shift of 3 units down (y-intercept = -3). [br][br][/b] [color=#0000ff]The new relation is [/color][b][color=#ff0000]y=x - 3[/color][/b] , [color=#0000ff]denoted by line f.[br] Set the slope of the relation to m=1 by entering 1 for m.[br] Set the y-intercept of the relation to b=-3 by entering -3 for b. [br] Set the x-intercept of the relation to c=0 by entering 0 for c. [br][/color][b]Observe the transformation of the linear relation.[/b]

When you change the y-intercept how does the graph change?

reflects the line across the x-axis shift line horizontally left or right compressess line shifts line vertically up or down stretches line

Exercise 3

[b]Perform the following linear relation transformation:[br][/b][br][b]Vertical stretch of the linear relation to 2. [br][br][/b] [color=#0000ff]The new relation is [/color][b][color=#ff0000]y=2x[/color][/b] , [color=#0000ff]denoted by line f.[br] Set the slope of the relation to 2 by entering 2 for m.[br] Set the y-intercept of the relation to b=0 by entering 0 for b. [br] Set the x-intercept of the relation to c=0 by entering 0 for c. [br][/color][b] Observe the transformation of the linear relation.[/b]

When you make the slope greater than 1 how does the graph change?

compressess line Reflects the line across the x-axis shifts line vertically up or down stretches line

Exercise 4

[b]Perform the following linear relation transformation:[br][/b][br][b]Vertical compression of the linear relation to 0.5. [br][br][/b] [color=#0000ff]The new relation is [/color][b][color=#ff0000]y=0.5x[/color][/b] , [color=#0000ff]denoted by line f.[br] Set the slope of the relation to 0.5 by entering 0.5 for m.[br] Set the y-intercept of the relation to b=0 by entering 0 for b. [br] Set the x-intercept of the relation to c=0 by entering 0 for c. [br][/color][b] Observe the transformation of the linear relation.[/b]

When you make the slope between 0 and 1 how does the graph change?

stretches line compressess line shifts line vertically up or down Reflects the line across the x-axis

Exercise 5

[b]Perform the following linear relation transformation:[br][/b][b][br]Vertical stretch and REFLECTION of the linear relation to - 1. [br][br][/b] [color=#0000ff]The new relation is [/color][b][color=#ff0000]y= - 1x[/color][/b] ,[color=#0000ff]denoted by line f. [/color][br][color=#0000ff] Set the slope of the relation to -1 by entering -1 for m.[br] Set the y-intercept of the relation to b=0 by entering 0 for b. [br] Set the x-intercept of the relation to c=0 by entering 0 for c. [br][/color][b] Observe the transformation of the linear relation.[/b]

When you make the slope a negative integer how does the graph change?

compressess line shifts line vertically up or down stretches line Reflects the line across the x-axis shifts line horizontally left and right

Exercise 6

[b][b]Perform the following linear relation transformation:[br][/b][br]Horizontal shift of the linear relation by 4[br][br][/b] [color=#0000ff]The new relation is [/color][b][color=#ff0000]y= (x+4) [/color][/b] , [color=#0000ff]denoted by line f[/color]. [br][color=#0000ff] Set the slope of the relation to 0 by entering zero for m.[br] Set the y-intercept of the relation to b=0 by entering 0 for b. [br] Set the x-intercept of the relation to 4 by entering 4 for c. [br][/color][b] Observe the transformation of the linear relation. [/b][br]

Exercise 7

[b][b]Perform the following linear relation transformation:[br][/b][br]Horizontal shift of the linear relation by -4[br][br][/b] [color=#0000ff]The new relation is [/color][b][color=#ff0000]y= (x-4) [/color][/b] , [color=#0000ff]denoted by line f[/color]. [br][color=#0000ff] Set the slope of the relation to 0 by entering zero for m.[br] Set the y-intercept of the relation to b=0 by entering 0 for b.[br] Set the x-intercept of the relation to 4 by entering 4 for c. [br][/color][b] Observe the transformation of the linear relation. [/b][br]

When you make change c how does the graph change?

shifts line horizontally left and right shifts line vertically up or down stretches line Reflects the line across the x-axis compressess line

Putting it all together

[b][b]Perform the following linear relation transformation:[br][/b][/b][br][color=#0000ff]The new relation is [/color][b][color=#ff0000]y= -1(x-4)+3 [/color][/b] , [color=#0000ff]denoted by line f[/color]. [br]

Describe all the transformations to the line y=x