Linear Transformations

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 f(x) + 2?

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

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

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

• Up 7
• Down 7
• Left 7
• Right 7

Which represents the parent function shifted down two units?

• f(x) = -2x

• f(x) = x - 2

• f(x) = x + 2

• f(x) = 2x

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 by a factor of 1/5

• Graph g shifted down 1 unit

• Graph g is steeper by a factor of 1/5

• Graph g shifted up 2 units

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

• Shifts the graph left four units

• Shifts the graph right four units

• Shifts the graph up four units

• Shifts the graph down four units

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

What are the transformations shown here?

3f(x) - 2

• more steep, down 2

• less steep, down 2

• more steep, reflection

• more steep, up 2

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