Linear Function Transformations

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

• g(x) is translated up 6 units

• g(x) is translated down 6 units

• g(x) is translated left 6 units

• g(x) is translated right 6 units

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 translated down 2 units.

• Graph g is steeper.

• Graph g is less steep.

Describe the transformation from the parent function: y = 3x + 5

• Steeper; translated up 5 units

• Steeper; translated down 5 units

• Less steep; translated up 5 units

• Less steep; translated down 5 units

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

• Graph g rotated

• Graph g translated down 4 units

• Graph g translated up 4 units

• Graph g reflected

How does the graph of g(x) compare to f(x)?

• g(x) is steeper and translated down from f(x)

• g(x) is steeper and translated up from f(x)

• g(x) is less steep and translated down from from f(x)

• g(x) is less steep and translated up from f(x)

Rewrite f(x) = 2x - 1 translated up three units and the slope doubled

• f(x) = 5x - 2

• f(x) = 4x + 2

• f(x) = 4x + 3

• f(x) = 5x - 4

Describe the transformation(s) from f(x) to g(x).

f(x) = 3x - 5

g(x) = -3x + 2

• Rotation steeper and translated up 7

• Rotation less steep and translated up 7

• Reflection and translated up 7

• Reflection and translated down 7 units

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

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 4 units up from the graph f

• The graph of g is a horizontal translation of the graph of f, 4 units right

• The graph of g is a horizontal translation of the graph of f, 4 units left

• The graph of g is a vertical stretch of the graph of f, by a factor of 7

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