Shifting Functions

Which quadratic function is represented by the graph?

• y = 2(x - 4)² + 5

• y = 2(x + 4)² + 5

• y = -2(x - 4)² + 5

• y = -2(x + 4)² + 5

Tags

CCSS.HSF-IF.C.7A

The graph shows the function f(x)=x³ in blue and another function g(x) in red.  Which could be the equation for g(x)?

• g(x) = -x³

• g(x) = x³ - 1

• g(x) = (x + 1)³

• g(x) = (x - 1)³

Tags

CCSS.HSF.BF.B.3

• y=(x+8)²

• y=(x-8)²

• y=x²+8

• y=x²-8

• g(x)=2x²
• g(x)=0.5x²
• g(x)=x²+2
• g(x)=(x+2)²

Identify the transformation from the graph of f(x)=x² to the graph g(x)= (x+5)² 

• shifted up five units

• shifted down five units

• shifted left 5 units

• shifted right 5 units

Describe the transformations of f(x) when compared to the parent function.
f(x)=x²+5

• horizontal shift right 5 units

• horizontal shift left 5 units

• vertical shift up 5 units

• vertical shift down 5 units

What would the equation for the new quadratic function be if it was vertically shifted up 3 units  from the function f(x)=4x²+2?

•  g(x)=x²+3

•  g(x)=7x²+2

•  g(x)=4x²+3

•  g(x)=4x²+5

What would the equation for the new quadratic function be if it was horizontally shifted right 1 unit  from the function f(x)=x²+4?

• g(x)=x²+5

• g(x)=(x+1)²+4

• g(x)=(x-1)²+4

• g(x)=x²+3

What is the equation of the quadratic function obtained from vertically stretching the parent function by a factor of 2 and then vertically shifting up 3 units?

• f(x)= 2(x-3)²

• f(x)= 2(x+3)²

• f(x)= 2x²+3

• f(x)= (x-2)²+3

If red represents y = x², which equation represents blue?

• y = 2x²

• y = -2x²

• y = -x²

• y = (x - 1)²