Understanding Radical Functions and Transformations

What does the parameter 'a' affect in the graph of a radical function?

• The horizontal shift

• The vertical shift

• The sharpness of the curve

• The starting point

Which step is NOT part of graphing a radical function?

• Making a table of values

• Calculating the domain and range

• Finding the x-intercepts

• Connecting points with a smooth curve

What is the starting point of the function y = √x + 5?

• (5, 0)

• (0, 5)

• (5, 5)

• (0, 0)

How does the graph of y = √x + 5 differ from the parent function y = √x?

• It becomes wider

• It reflects over the x-axis

• It shifts 5 units up

• It shifts 5 units to the right

What is the domain of the function y = √(x-2) - 1?

• x ≤ 0

• x ≤ 2

• x ≥ 2

• x ≥ 0

What transformation occurs in the function y = √(x-2) - 1 compared to y = √x?

• Left 1, up 2

• Right 2, down 1

• Left 2, up 1

• Right 1, down 2

What effect does a negative 'a' value have on the graph of a radical function?

• It shifts the graph up

• It shifts the graph down

• It reflects the graph vertically

• It makes the graph wider

In the function y = 2√x + 3, what does the '2' do to the graph?

• Makes it wider

• Shifts it up

• Makes it narrower

• Shifts it down

What is the range of the function y = -√(x-1) + 4?

• y ≥ 4

• y ≥ 0

• y ≤ 0

• y ≤ 4

How does the graph of y = -√(x-1) + 4 differ from the parent function y = √x?

• It shifts left 1 and up 4, and reflects horizontally

• It shifts right 1 and down 4, and reflects horizontally

• It shifts left 1 and down 4, and reflects vertically

• It shifts right 1 and up 4, and reflects vertically