Transformations of Linear and Quadratic Functions

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.

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

• Shifted up 2 units

• Shifted down 2 units

• Shifted right 2 units

• Shifted 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.

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

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

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)

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

What is the linear parent function?

• f(x) = x 
• y = mx + b 
• f(x) = 2x 
• f(x)  = y