Transformations and Domain and Range

What is the domain?

• [ -2 , 2 ]

• [ 4 , -4 ]

• all real numbers

• [-2, 4]

What is the range? 

• (-∞, -3]

• [0, 3]

• [0, +∞)

• [3, +∞)

Match the equation to its description.

• Right 2 and up 2

• Left 2 and up 2

• Right 2 and down 2

• Left 2 and down 2

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

What are the transformations of this functions compared to the parent function y = √(x)?

• Shifted right 5, shifted down 2, and flipped

• Flip, stretch by 2, and shifted right 5

• Flip, shrink by 2, and shifted left 5

• Shifted right 5, shifted down 2

DOMAIN?

• all real numbers

• [0,∞)

• (-∞,0]

• -2, 2

• reflects over x axis, vertical stretch by 3, right 2, up 1

• reflects over y axis, vertical compression by -3, left 2, up 1

• reflects over x axis, vertical stretch by -3, left 2, up 1

• reflects over y axis, vertical compression by 1/3, right 2, up 1

Find the domain and range of the function
Hint: use the calculator to see the graph
f\left(x\right) = -\sqrt{x-1}+4

• Domain: (-∞, ∞) Range: [-∞, 4]

• Domain: [1, ∞) Range: (-∞, 4]

• Domain: [-1. ∞) Range: [4, ∞) 

• Domain: [4, ∞) Range: [-1,∞) 

What is the domain of the function in this graph?

• (-infinity, 3]

• [3, inifinity)

• (-infinity, 0]

• [0, infinity)

• Vertical Compression by 2

• Vertical Stretch by 2

• Vertical Compression by 1/2

• Horizontal Stretch by 2