Linear Equations and Transformations

linear transformations

Open Ended

Which graph does not belong and why?

Multiple Choice

What is the equation for the parent linear function?

• y = 2x

• y = x

• y = ¼x

• y = x²

Multiple Choice

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

• Up 7

• Down 7

• Less steep

• Steeper

Multiple Choice

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

• Shift up 2

• Shift down 2

• steeper

• flipped

Multiple Choice

Which represents the parent function shifted down two units?

• f(x) = -2x

• f(x) = x - 2

• f(x) = x + 2

• f(x) = 2x

Multiple Choice

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

• The graph of g is a vertical translation 2 units up of the graph of f

• The graph of f is a horizontal translation two units left of g

• The graph of g is a vertical stretch by a factor of 2 of the graph of f

• The graph of g is a reflection of the graph of f

Multiple Choice

What transformation has occurred:

$$y=-\left(x\right)$$  

• Vertical Stretch of 3

• Reflected over the x-axis

• Left 3

• Up 3

Multiple Choice

Describe the transformations from the parent function.

• Flatter/Vertical compress and down 3 units

• Flatter/Vertical compress and up 3 units

• Steeper/Vertical stretch and down 3 units

• Steeper/Vertical stretch and up 3 units

Multiple Choice

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

• Vertical stretch by a factor of 2

• Vertical compression by a factor of 1/2

• Vertical translation up by 2 units.

• Horizontal compression by a factor of 1/2

Multiple Choice

Describe the transformation from the parent function.

• Shift up 1/2 units

• Steeper/Vertical stretch

• Reflection across the y-axis

• Flatter/Vertical compress

Multiple Choice

A student graphed f(x) = x and g(x) = ⅓f(x). Which statement is true?

• The graph of f is steeper than the graph of g.

• The graph of f is less steep than the graph of g.

• The graph of f is shifted 2 units up to create the graph of g.

• The graph of f is shifted 2 units to the right to create the graph of g.

Multiple Choice

The linear parent function, f(x) = x, is transformed to g(x) = f(x + 6). Describe the transformation.

• g(x) is shifted up 6 units

• g(x) is shifted down 6 units

• g(x) is shifted left 6 units

• g(x) is shifted right 6 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

Which of the following represents horizontal stretches and compressions?

• f(x)+d
• f(x-c)
• f(bx)
• af(x)

Multiple Choice

what is this transformation f(3x)

• Horizontal stretch by 3

• Horizontal stretch by 1/3

• Horizontal Compression by 3

• Horizontal compression by 3

Multiple Choice

Which transformation on

f(x) = x

is g(x) = f(-x)

• Reflection across the y-axis

• The slope will be less steep

• The graph will be wider

• Reflection across the x-axis.

Multiple Choice

Which equation transforms f(x) = x to a horizontal stretch by a factor of 2, a reflection over the x axis, and a shift down 4?

• f(-2x - 4)

• f(-1/2x) - 4

• -f(2x) - 4

• -f(1/2x) - 4

Multiple Choice

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

• Reflection over x-axis, steeper, up 5

• Reflection over y-axis, less steep, right 5

• Steeper, left 5

• reflection over x-axis, less steep, up 5

Multiple Choice

How did the equation f(x) = x change if

g(x) = 1/2f(x) + 11

• Vertical stretch and shift up 11

• Horizontal shrink and shift down 11

• Vertical shrink and shift up 11

• Horizontal stretch and shift down 11