Exploring Transformations in Mathematics

The video tutorial explains how any function can be derived from parent functions through transformations. It covers three types of transformations: translations, dilations, and reflections. Each type is explained in detail, with examples provided for graphing transformed functions, including square root, absolute value, and cube root functions. The tutorial also demonstrates how to use a graphing calculator to visualize these transformations.

What are the three types of transformations discussed in the video?

• Translations, Dilations, Rotations

• Translations, Dilations, Reflections

• Translations, Rotations, Reflections

• Translations, Reflections, Rotations

What does adding a number inside the parentheses with x do to the graph?

• Shifts the graph left

• Shifts the graph down

• Shifts the graph right

• Shifts the graph up

If a number is added outside the parentheses with x, what is the effect on the graph?

• Shifts the graph left or right

• Shifts the graph up or down

• Compresses the graph vertically

• Stretches the graph vertically

What is a vertical stretch?

• Shifting the graph right

• Making the graph shorter and wider

• Making the graph taller and narrower

• Shifting the graph left

How do you know if a function will undergo a vertical compression?

• The absolute value of the number in front is less than one

• The number in front is positive

• The number in front is negative

• The absolute value of the number in front is greater than one

What does a negative sign in front of the function indicate?

• A reflection over the y-axis

• A reflection over the x-axis

• A vertical compression

• A vertical stretch

What happens to the graph when it is reflected over the x-axis?

• It shifts to the left

• It remains unchanged

• It shifts to the right

• It flips upside down

In the example of graphing a quadratic function, what is the new vertex after shifting left one unit and up four units?

• (-1, 4)

• (1, -4)

• (-1, -4)

• (1, 4)

How do you enter a square root function in a graphing calculator?

• Use the 'math' button and select 'sqrt'

• Use the 'alpha' button and select 'sqrt'

• Use the 'graph' button and then the 'sqrt' key

• Use the 'second' button and then the 'squared' key

What is the effect of a vertical stretch by a factor of 2 on the graph?

• The graph shifts down by 2 units

• The graph becomes shorter and wider

• The graph becomes taller and narrower

• The graph shifts up by 2 units