Transformations on a Graph

Which equation below is a quadratic function translated up 5 units?

• y = x² + 5
• y = (x + 5)²
• y = 5x²
• y = -x² - 5

The graph shows the function f(x)=x² in blue and another function g(x) in red.  Which could be the equation for g(x)?

• A.  g(x) = 2x²
• B.  g(x) = 1/2x²
• C.  g(x) = x² + 2
• D.  g(x) = (x + 2)²

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

Name the parent function.

• linear
• quadratic
• cubic
• logarithmic

If f(x) is the red graph and g(x) is the blue graph, what transformation changes f(x) to g(x)?

• translation

• rotation

• reflection

• vertical stretch

Which function DOES NOT represent a horizontal shift of the function f(x)=x²

• g(x)= x²+3

• g(x)= (x+3)²

• g(x)= (x-3)²

• g(x) =(x-2)²

• The function is being moved 4 units to the right

• The function is being moved 12 units to the left

• The function is being moved 4 units to the left

• The function is being 12 units to the right

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

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

Describe the transformation that occurred

g(x) =2f(x)

• Up 2 units

• vertical compression

• vertical stretch

• Right 2 Units