Understanding Transformed Square Root Functions

This video tutorial explains how to find the equation of a transformed square root function. It begins by identifying the transformations applied to the basic square root function, such as reflection across the y-axis and shifts. The tutorial then demonstrates how to write the transformed function using function notation and verifies the transformations by graphing the function on a calculator. Key points include the importance of parentheses in transformations and common errors to avoid.

What is the starting point of the basic square root function?

• (0,0)

• (-3,-2)

• (-2,-3)

• (2,3)

Which transformation reflects a function across the Y-axis?

• Y = F(-X)

• Y = F(X - C)

• Y = F(X + C)

• Y = F(X) - D

How does a positive constant inside the function affect a horizontal shift?

• No shift

• Reflects the graph

• Shifts the graph left

• Shifts the graph right

What is the effect of a vertical shift on the function?

• Reflects across the X-axis

• No effect

• Shifts the graph up or down

• Shifts the graph left or right

What is the correct form of G(x) after applying a reflection and a left shift?

• G(x) = F(-X - 2)

• G(x) = F(-X + 2)

• G(x) = F(X + 2)

• G(x) = F(X - 2)

What is the final equation for G(x) after all transformations?

• G(x) = √(-X + 2) - 3

• G(x) = √(X - 2) + 3

• G(x) = √(X + 2) - 3

• G(x) = √(-X - 2) + 3

What tool is used to verify the transformed function?

• Graphing calculator

• Protractor

• Ruler

• Calculator

What happens if parentheses are omitted in the transformation?

• The graph shifts 2 units right

• The graph shifts 2 units left

• The graph reflects across the X-axis

• The graph remains unchanged

Why is it important to use parentheses in transformations?

• To ensure correct order of operations

• To simplify the equation

• To make the equation look neat

• To avoid syntax errors

What is a common mistake when setting up the function with multiple transformations?

• Using the wrong variable

• Omitting parentheses

• Forgetting to add constants

• Incorrectly labeling axes