Exploring Non-Rigid Transformations of Functions

The video tutorial covers transformations of functions, focusing on non-rigid transformations like vertical stretches and compressions. It explains how coefficients affect the graph's shape, using parabolas, cubic, and absolute value functions as examples. The tutorial also demonstrates how to derive functions from graphs and emphasizes the correct order of applying transformations.

What type of transformation does a coefficient greater than one cause?

• Vertical compression

• Reflection

• Horizontal shift

• Vertical stretch

If a coefficient is between zero and one, what transformation occurs?

• Reflection

• Vertical compression

• Horizontal shift

• Vertical stretch

What is the effect of a negative coefficient on the graph of a function?

• Vertical stretch

• Horizontal shift

• Vertical compression

• Reflection

How does a vertical stretch affect the steepness of a parabola?

• No change

• Makes it steeper

• Shifts it horizontally

• Makes it flatter

What transformation is applied when the coefficient is one-half?

• Horizontal shift

• Reflection

• Vertical compression

• Vertical stretch

In a cubic function, what does a negative coefficient inside the function indicate?

• Vertical stretch

• Horizontal shift to the right

• Horizontal shift to the left

• Reflection across the y-axis

How do you determine the new position of a point after a transformation?

• Multiply the y-value by the coefficient

• Add the coefficient to the x-value

• Subtract the coefficient from the y-value

• None of the above

What does a graph look like when a function has a square root transformation with a negative coefficient?

• It is flipped across the x-axis

• It remains unchanged

• It is stretched vertically

• It is compressed vertically

Which transformation involves multiplying the y-values by a factor and then adjusting vertically?

• Horizontal shift

• Vertical stretch

• Reflection

• All of the above

What is the correct sequence of applying transformations to a function?

• Horizontal, Vertical, Reflection

• Horizontal, Reflection, Vertical

• Reflection, Vertical, Horizontal

• Vertical, Horizontal, Reflection