Transformations of Functions and Domain and Range

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

Which transformation transforms the graph of
f(x) = x² to the graph of
g(x) = (x + 4)²?

• a vertical translation 4 units up
• a vertical translation 4 units down
• a horizontal translation 4 units to the left
• a horizontal translation 4 units to the right

How did we transform from f(x) =x² 
to
g(x) = -3x²

• reflection in x-axis and vertical shift down
• reflection x-axis and vertical stretch
• horizontal stretch
• reflection x-axis and vertical compression

How did we transform from the parent function?
g(x) = -1/5(x - 1)² + 7

• reflection, vertical compression, horizontal right, vertical up
• vertical compression, horizontal shift left, vertical shift up
• reflection, horizontal shift right, vertical shift down
• no changes were made to y = x²

In the equation f(x)=5(x+3)²-10 what does the 5 do?

• Vertical stretch by 5
• Horizontal compress by 5
• Reflect
• Move up 5

What is the vertical shift of this equation?
f(x) = -(x + 3)² - 5

• left 5
• right 5
• up 5
• down 5

What is the vertical shift of this equation?
g(x) = 3/4 (x - 5)² + 12

• up 12
• down 12
• left 12
• right 12

What transformations have occurred? 

• Right 2 and up 2
• Left 2 and up 2
• Right 2 and down 2
• Left 2 and down 2

What the is the domain of y=x²

• All real numbers

• x>0

• x<0

• x=0

What the is the range of y=x²

• All real numbers

• [0, infinity)

• (-infinity, 0]