Function Transformations and Their Effects

The video tutorial covers transformations in mathematics, focusing on exponential functions. It begins with an introduction to transformations, followed by detailed explanations of vertical and horizontal translations, stretches, and compressions. The tutorial includes a crash course on transformation concepts and explores the basics of exponential functions, including graphing and asymptotes. The video concludes with a discussion on combining different transformations and their effects on graphs.

What is the primary difference between a transformation and a translation?

• A translation involves rotation.

• They are the same.

• A transformation is a type of translation.

• A translation is a type of transformation.

How does a vertical translation affect the graph of a function?

• It stretches the graph vertically.

• It shifts the graph up or down.

• It shifts the graph left or right.

• It compresses the graph horizontally.

What happens to the graph of a function during a horizontal compression?

• The graph shifts downwards.

• The graph becomes narrower.

• The graph becomes wider.

• The graph shifts upwards.

Which of the following is true about the parent function in transformations?

• It is a function that only shifts vertically.

• It is a function with no asymptotes.

• It is the original function before any transformations.

• It is the final transformed function.

How does a vertical shift affect the horizontal asymptote of a function?

• It moves the asymptote left or right.

• It eliminates the asymptote.

• It moves the asymptote up or down.

• It does not affect the asymptote.

What is the effect of multiplying a function by a factor greater than 1?

• It stretches the function vertically.

• It reflects the function over the x-axis.

• It shifts the function horizontally.

• It compresses the function vertically.

What does a horizontal stretch by a factor of 1/2 imply?

• Multiply each x-coordinate by 2.

• Divide each x-coordinate by 2.

• Multiply each y-coordinate by 2.

• Divide each y-coordinate by 2.

In standard form, what does the 'C' in a * b^x + C represent?

• Vertical shift

• Vertical stretch

• Horizontal compression

• Horizontal shift