Graph Transformations and Effects

This video tutorial explains how to graph functions with multiple transformations, focusing on the effects of the values A, B, C, and D on the function. It provides a step-by-step guide to graphing transformations, including reflection, vertical and horizontal compression, and shifts. The video also covers a more complex example, demonstrating how to handle transformations not in the standard form. The tutorial emphasizes understanding parent functions to graph transformed functions easily without a calculator.

What does a negative value of A indicate in the transformation of a function?

• Vertical stretch

• Reflection about the x-axis

• Horizontal shift

• Vertical shift

If a function is vertically compressed by a factor of 1/2, what happens to the y-coordinates of the points?

• They are halved

• They remain the same

• They are inverted

• They are doubled

How do you shift a graph left by one unit?

• Subtract one from the y-coordinates

• Add one to the x-coordinates

• Subtract one from the x-coordinates

• Add one to the y-coordinates

In the complex example, what does a value of B equal to 2 indicate?

• Vertical shift

• Horizontal shift

• Vertical stretch

• Horizontal compression

What is the parent function for the complex example discussed?

• y = √x

• y = x^2

• y = 1/x

• y = |x|

What transformation occurs when C is negative?

• Shift left

• Shift down

• Shift right

• Shift up

What is the effect of adding a constant to the y-coordinate of a function?

• Compression

• Reflection

• Vertical shift

• Horizontal shift

How do you perform a horizontal compression on a graph?

• Divide the y-coordinates by A

• Multiply the x-coordinates by B

• Divide the x-coordinates by B

• Multiply the y-coordinates by B

What is the result of shifting a graph up by one unit?

• Subtract one from the x-coordinates

• Add one to the x-coordinates

• Add one to the y-coordinates

• Subtract one from the y-coordinates

What is the final step in graphing a transformed function?

• Check for symmetry

• Identify the parent function

• Apply all transformations

• Use a graphing calculator