Linear Transformations Translation

• Move lines up/down on graph.

• Changes the y intercept (positive shifts up; negative shifts down).

• Called a Vertical Shift.

Translations - Vertical

• Moves lines right/left on graph.

• Called a Horizontal Shift.

• Remember, "Your Ex always lies."

• The line shifts the opposite of what you would expect.

Translations - Horizontal

The new slope will be greater than 1.

This is called a Vertical Stretch.

Rotations - more steep

The new slope will be a fraction.

This is called a Vertical Compression or Shrink.

Rotations - less steep

• Flips the graph over the y-axis.

​

• Negative slope.​

• Forms an X.

Reflections

Multiple Choice

How did the equation shift from the parent function y = x to y = x + 2?

• translated up 2

• translated down 2

• steeper

• translated right 2

Multiple Choice

In order to determine if the linear function has shifted up or down (translated,) we look at the _____ in the equation or on the graph.

• x-intercept

• y-intercept

• slope

• negative slope

Multiple Choice

In order to determine if the linear function has compressed or stretched (rotated), we look at the _____ in the equation or on the graph.

• x-intercept

• y-intercept

• slope

• negative slope

Multiple Choice

In order to determine if the linear function has reflected (flipped), we look to see if the equation or graph has a ______.

• x-intercept

• y-intercept

• slope

• negative slope

Multiple Choice

The function f(x) = x

has been transformed to

g(x) = x - 5.

Which of the following describes the change?

• vertical shift up 5 units

• vertical shift down 5 units

• horizontal shift right 5 units

• horizontal shift left 5 units

Multiple Choice

What is the equation for the parent linear function?

• y = 2x

• y = x

• y = ¼x

• y = x²

Multiple Choice

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.

• Graph g is a reflection.

• Graph g shifts down 2 units.

• Graph g is steeper by a factor of 2

• Graph g is less steeper by a factor of 1/2

Multiple Choice

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.

• Graph g shifted down 3 units

• Graph g shifted down 4 units

• Graph g shifted up 4 units

• Graph g reflected

Multiple Choice

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.

• Graph g shifted down 6 units

• Graph g is steeper by a factor of 7

• Graph g is less steep by a factor of 1/3

• Graph g shifted up 6 units

Multiple Choice

What description is best represented by the graph of g?

• stretched by a factor of  $$\frac{1}{3}$$  

• compressed by a factor of  $$\frac{1}{3}$$  

• compressed by a factor of 3 
  

• stretched by a factor of 3

Multiple Choice

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.

• Graph g is less steep.

• Graph g shifted down 1 unit

• Graph g is steeper.

• Graph g shifted up 2 units

Multiple Choice

Describe the transformation that occurred from the parent function to 

$$g\left(x\right)\ =-\ 2x$$  

• Compressed by a factor of 2

• reflected over the y-axis and compressed by a factor of 2

• reflected over the y-axis and stretched by a factor of 2

• Stretched by a factor of 2

Multiple Choice

If the graph of the parent function f(x) = x is shifted 7 units up and is vertically compressed by a factor of 1/3, what is the equation for the function?

• g(x) = 7x + 1/3

• g(x) = 1/3x - 7

• g(x) = 1/3x + 7

• g(x) = 7x - 1/3

Multiple Select

What are the transformations shown here? Check all that apply

$$-x+3$$  

• reflection

• shifted down 3

• shifted up 3

• compressed by 3

Multiple Select

Select all the equations that have a translation from the parent function y = x.

• y = x + 5

• y = x - 2

• y = 2x

• y = 1/2x

Multiple Select

Select all the equations that have been reflected from the parent function y = x.

• y=x+5

• y=-x-2

• y= 2x

• y= -1/2x

Multiple Select

Select all the equations that are steeper than the parent function y = x.

• y = 3x + 5

• y = -x - 2

• y = 2x

• y = -1/2x

Multiple Select

Select all the equations that are less steep than then parent function y = x.

• y = 3x + 5

• y = 1/3x - 2

• y = 2x

• y = -1/2x

Multiple Choice

Describe the transformation of f(x) that results in g(x):
g(x) = f(x) - 4

• f(x) has been translated down 4.
• f(x) has been translated up 4.
• f(x) has been translated right 2
• f(x) has been translated left 2

Multiple Choice

Which transformation will occur if f(x) = x is replaced with  $$\frac{1}{4}f\left(x\right)$$  ?

• Vertical stretch by a factor of 4

• Vertical compression by a factor of 1/4

• Vertical translation up by 1/4 units.

• Horizontal compression by a factor of 1/4

Multiple Choice

Describe the transformation of f(x) that results in g(x):
g(x) = f(x - 4)

• f(x) has been translated to the right 4.
• f(x) has been translated to the left 4.
• f(x) has been translated up 4.
• f(x) has been translated down 4.

Multiple Choice

Which of the following shows the transformation of left 3, down 1?

• f(x+3) - 1
• f(x-3) - 1
• f(x-1) - 3
• f(x+1) + 3

Multiple Choice

Which transformation will occur if f(x) = x is replaced with f(x) + 2?

• Translation left 2 units
• Translation right 2 units
• Vertical translation up by 2 units.
• Reflection across the x-axis.

Multiple Choice

How did the equation shift from the parent function? y = f(x + 7)

• Up 7
• Down 7
• Left 7
• Right 7

Multiple Choice

How did the equation shift from the parent function? y = f(x - 4)

• Shift right by 4

• Shift left by 4

• Horizontal Stretch by 4

• Vertical Stretch by 4

• Shift down by 4

Multiple Choice

How did the equation shift from the parent function? y = (x - 3) + 5

• 3 right, 5 up
• 3 left, 5 up
• 3 Down
• Moved 5 right

Multiple Choice

How did the equation shift from the parent function? y = (x - 4)

• Shift right by 4
• Shift left by 4
• Horizontal Stretch by 4
• Vertical Stretch by 4

Multiple Choice

If the graph of the parent function f(x) = x is shifted 7 units up 5 left, what is the function?

• f(x) = (x+5)+7
• f(x) = (x+7)-5
• f(x) = x+12
• f(x) = 7x - 3

Multiple Choice

The linear parent function, f(x) = x, is transformed to g(x) = f(x - 3). Describe the transformation.

• g(x) is shifted up 3 units

• g(x) is shifted down 3 units

• g(x) is shifted left 3 units

• g(x) is shifted right 3 units

Multiple Choice

The linear parent function, f(x) = x, is transformed to g(x) = f(x + 3). Describe the transformation.

• g(x) is shifted up 3 units

• g(x) is shifted down 3 units

• g(x) is shifted left 3 units

• g(x) is shifted right 3 units

Multiple Choice

The linear parent function, f(x) = x, is transformed to g(x) = f(x) - 3. Describe the transformation.

• g(x) is shifted up 3 units

• g(x) is shifted down 3 units

• g(x) is shifted left 3 units

• g(x) is shifted right 3 units

Multiple Choice

What is the linear parent function?

• f(x) = x 
• y = mx + b 
• f(x) = 2x 
• f(x)  = y 

Multiple Choice

Which transformation will occur if y = x is replaced with y = 2x?

• Vertical stretch

• Vertical compression

• Vertical translation up by 2 units.

  Horizontal stretch

• Horizontal compression

Poll

Are you Clear or Cloudy on this lesson?

• I am Clear. I could teach it to others.

• I am Cloudy. I should re-do this lesson.