Transformation of Functions

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 vertical translation 2 units down of the graph of f

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

  The blue function is the original function f(x) = x³.  Which of the following is the correct equation for the red function, g(x)?

• g(x) = x³ + 1

• g(x) = x³ - 1

• g(x) = (x - 1)³

• g(x) = (x + 1)³

Tags

CCSS.HSA.SSE.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Identify the transformation(s) from the graph of f(x) to the graph g(x) = -f(x + 5).

• shifted up five units
  reflection across the x-axis

• shifted down five units
  reflection across the x-axis

• shifted left 5 units
  reflection across the x-axis

• shifted right 5 units
  reflection across the x-axis

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.5

Given g(x) = f(x - 3) + 5.  What transformations took place from the original function f(x)?

• shift left 3 and up 5

• shift right 3 and down 5

• shift left 3 and down 5

• shift right 3 and up 5

Tags

CCSS.HSF.BF.B.3

 f(x) is transformed so that it maps onto g(x). Which equation would correctly represent g(x)

• g(x)=2f(x)
• g(x)=0.5f(x)
• g(x)=f(x) + 2
• g(x)=f(x + 2)

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

g(x) = f(x) - 4

• vertical shift

  down 4

• horizontal shift right 4

• vertical shift up 4

• horizontal shift left 4

Tags

CCSS.HSF.BF.B.3

g(x) = f(x + 4)

• vertical translation down 4

• horizontal translation right 4

• vertical translation up 4

• horizontal translation left 4

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

g(x) = f(x - 4)

• horizontal translation right 4

• vertical translation down 4

• horizontal translation left 4

• vertical translation up 4

Tags

CCSS.HSF.BF.B.3

g(x) = -f(x)

• vertical compression by a factor of -1

• reflection across the y-axis

• vertical stretch by a factor of -1

• reflection across the x-axis

Tags

CCSS.HSF.BF.B.3

g(x) = 4f(x)

• refection across the x-axis

• vertical compression by a factor of 4

• vertical stretch by a factor of 4

• shift up 4

Tags

CCSS.HSF.BF.B.3