Exploring Transformations of Functions

The video tutorial introduces transformations of functions, focusing on the square root function. It covers vertical and horizontal shifts, reflections over the x and y axes, and vertical stretches and compressions. The tutorial uses examples to illustrate how these transformations affect the graph of a function, providing a comprehensive understanding of function transformations.

What is the parent function discussed in the video?

• y = 1/x

• y = sqrt(x)

• y = |x|

• y = x^2

What does a minus sign at the end of the function y = sqrt(x) - 2 indicate?

• A horizontal shift to the left

• A vertical shift up

• A horizontal shift to the right

• A vertical shift down

If you have a plus sign inside the function y = sqrt(x + 2), what kind of shift does it represent?

• A horizontal shift to the left

• A vertical shift down

• A horizontal shift to the right

• A vertical shift up

What does a negative sign in front of the function y = -sqrt(x) indicate?

• A reflection over the y-axis

• A horizontal shift to the right

• A reflection over the x-axis

• A vertical shift up

In the function y = sqrt(-x), what does the negative sign inside the square root indicate?

• A horizontal shift to the right

• A reflection over the y-axis

• A reflection over the x-axis

• A vertical shift down

What does a vertical stretch do to the graph of a function?

• Makes it skinnier

• Makes it wider

• Makes it shorter

• Makes it taller

If 'a' in y = a * sqrt(x) is greater than 1, what transformation occurs?

• Horizontal compression

• Horizontal stretch

• Vertical stretch

• Vertical compression

What does a coefficient of 'B' in a function indicate?

• Horizontal stretch or compression

• Vertical stretch

• Reflection over the x-axis

• Vertical compression

In the example of y = 2x^2, what does the coefficient 2 represent?

• Horizontal stretch

• Horizontal compression

• Vertical stretch

• Vertical compression

What is the effect of a vertical stretch on a graph with fixed endpoints?

• Makes the graph skinnier

• Makes the graph wider

• Increases the slope of the sides

• Decreases the slope of the sides