Understanding Transformations of Square Root Functions

The video tutorial explains how to determine the equation of a transformed square root function by analyzing corresponding points on the original and transformed graphs. It demonstrates the process of identifying shifts in the function and verifying the equation using a graphing calculator. The tutorial provides a step-by-step approach to understanding function transformations and ensures the accuracy of the derived equation through practical verification.

What is the main goal of the tutorial?

• To understand the properties of square root functions.

• To determine the equation of a transformed square root function.

• To compare different types of functions.

• To learn how to graph square root functions.

Which points are initially considered on the basic square root function?

• (0,0) and (4,2)

• (1,1) and (3,3)

• (2,2) and (5,5)

• (0,0) and (2,2)

What are the coordinates of the corresponding points on the transformed function?

• (0,1) and (4,3)

• (3,4) and (7,6)

• (1,2) and (5,4)

• (2,3) and (6,5)

How has the blue function been transformed from the red function?

• Shifted left three units and down two units.

• Shifted right three units and up two units.

• Shifted left two units and down three units.

• Shifted right two units and up three units.

What is the equation of the transformed function?

• G(x) = √(x - 3) + 2

• G(x) = √(x + 3) - 2

• G(x) = √(x - 2) + 3

• G(x) = √(x + 2) - 3

What is the purpose of using a graphing calculator in this tutorial?

• To verify the derived equation of the transformed function.

• To draw the basic square root function.

• To calculate the slope of the function.

• To find the intersection points of the functions.

What should be the X MIN and X MAX settings on the graphing calculator?

• -5 and 15

• 0 and 8

• -2 and 10

• -10 and 20

What should be the Y MIN and Y MAX settings on the graphing calculator?

• -2 and 8

• -10 and 20

• -5 and 15

• 0 and 10

Which points are verified on the graphing calculator to confirm the equation?

• (1,2) and (5,4)

• (2,3) and (6,5)

• (3,4) and (7,6)

• (0,1) and (4,3)

What is the final step in verifying the equation of the transformed function?

• Checking the slope of the function.

• Ensuring the graph matches the expected transformation.

• Calculating the derivative of the function.

• Finding the y-intercept of the function.