Transformations of Linear and Quadratic Functions

Identify the transformation from the graph of f(x)=x² to the graph g(x)= f(0.5x). 

• horizontal compression
• horizontal stretch
• horizontal translation up 0.5 units
• vertical stretch

Identify the transformation from the graph of f(x)=x² to the graph g(x)= -f(x). 

• reflection over the x-axis
• reflection over the y-axis
• vertical stretch
• The graphs are the same.

Tags

CCSS.HSF.BF.B.3

Identify the transformation from the graph of f(x)=x to the graph g(x)= f(x-2). 

• horizontal stretch
• horizontal compression
• horizontal shift right 2 units
• horizontal shift left 2 units

A student graphed f(x) = x and g(x) = 3f(x) on the same coordinate grid.  Which statement describes how the graphs are related?

• f(x) is shifted 3 units up to create g(x)
• f(x) is less steep than g(x)
• f(x) is steeper than g(x)
• The graphs are the same.

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.C.7

Identify the transformation from the graph of f(x)=x  to the graph g(x)= f(x) + 4

• vertical shift up 4 units
• vertical shift down 4 units
• vertical stretch by a factor of 4
• vertical compression by a factor of 4

Tags

CCSS.HSF.BF.B.3

If the blue is f(x)=x^2, the red must be

• g(x)=(x+3)²
• g(x)=(x-3)²
• g(x)=x²+3
• g(x)=x²-2

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

If f(x)=x² is the dashed yellow graph, then the blue graph is 

• g(x) = x²-C
• g(x) = (x+C)²
• g(x) = (x-C)²
• g(x) = x²+C

Which function describes the transformation of shifting f(x)=x² two units right?

• h(x) = x² + 2
• h(x) = x² - 2
• h(x) = (x + 2)²
• h(x) = (x - 2)²

 f(x) in blue is transformed so that it maps onto g(x) in red.  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.C.7

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.4

CCSS.HSG.CO.A.5

If the blue is f(x)=x^2, then the red must be

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

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11