Exploring Linear Transformations

The video tutorial explores the effects of slope on graph transformations. It begins by discussing how slopes greater than one stretch the graph towards the y-axis, while slopes between zero and one compress it. The focus then shifts to negative slopes, explaining how they cause a reflection over the x-axis. The instructor demonstrates this by graphing a line with a negative slope and using paper folding to visualize the reflection. The tutorial concludes by emphasizing the concept of reflection and its impact on graph orientation.

What happens to the graph of a line when the slope is greater than one?

• It remains unchanged.

• It stretches closer to the y-axis.

• It flips over the x-axis.

• It compresses away from the y-axis.

If the slope of a line is between zero and one, what transformation occurs?

• The line compresses away from the y-axis.

• The line remains unchanged.

• The line stretches closer to the y-axis.

• The line flips over the x-axis.

What is the first step when dealing with a negative slope?

• Graph the line without considering the negative sign.

• Ensure the reflection is over the x-axis.

• Change the slope to a positive value.

• Ignore the y-intercept.

What is the y-intercept used in the example for graphing a negative slope?

• 2

• 0

• -1

• 1

What is the result of multiplying -1 by 2 in the example?

• 1

• 0

• -2

• 2

What does the graph of y = -x look like compared to its parent function?

• It is a reflection over the x-axis.

• It is a reflection over the y-axis.

• It is a vertical line.

• It is a horizontal line.

What happens when you fold the graph of y = -x over the x-axis?

• It becomes a horizontal line.

• It remains unchanged.

• It matches the parent function.

• It becomes a vertical line.

What is the term used to describe the transformation of flipping over the x-axis?

• Dilation

• Rotation

• Translation

• Reflection

What does a negative slope indicate in terms of graph transformation?

• Compression

• Stretching

• Reflection over the x-axis

• No transformation

Can a reflection occur over the y-axis as well?

• Only if the slope is positive.

• Yes, always.

• No, never.

• Yes, but it depends on the context.