Transformations of Square Root Functions

The video tutorial explains how to transform the graph of f(x) = -√(x + 3) from the parent graph y = √x. It covers the effects of a negative sign outside the function, which causes a vertical reflection across the x-axis, and a plus 3 inside the function, which results in a horizontal shift to the left. The tutorial combines these transformations and guides viewers to identify the correct answer from multiple-choice options.

What is the parent graph of the function f(x) = -√(x + 3)?

• y = x + 3

• y = -x

• y = x^2

• y = √x

What does the negative sign outside the square root function indicate?

• A horizontal shift

• A vertical stretch

• A horizontal reflection

• A vertical reflection

In which axis does the graph reflect due to the negative sign outside the function?

• z-axis

• No reflection

• y-axis

• x-axis

What is the effect of a negative sign outside a function on its graph?

• It causes a horizontal reflection

• It causes a vertical shift

• It causes a vertical reflection

• It causes a horizontal shift

Which axis is involved in the reflection of the graph of f(x) = -√(x + 3)?

• No axis

• z-axis

• y-axis

• x-axis

What is the effect of the +3 inside the square root function?

• Shift 3 units up

• Shift 3 units down

• Shift 3 units to the left

• Shift 3 units to the right

How does a horizontal shift inside a function typically behave?

• It moves opposite to the direction of the sign

• It does not cause any shift

• It moves in the direction of the sign

• It causes a vertical shift

Which transformation should be applied first according to the order of operations?

• Horizontal reflection

• Vertical shift

• Horizontal shift

• Vertical reflection

What is the final transformation sequence for the function f(x) = -√(x + 3)?

• Shift right, reflect in y-axis

• Shift left, reflect in x-axis

• Shift up, reflect in x-axis

• Shift down, reflect in y-axis

How does the graph of y = √x change when transformed to f(x) = -√(x + 3)?

• It shifts up and reflects in the x-axis

• It shifts left and reflects in the x-axis

• It shifts right and reflects in the y-axis

• It shifts down and reflects in the y-axis