Graph Transformations and Their Effects

This video tutorial explores transformations in cubic and quadratic graphs, focusing on dilations, reflections, and translations. It explains how these transformations affect the graphs and how to identify them from equations. The tutorial provides examples and step-by-step explanations to help understand the mathematical concepts involved.

What is the primary focus of the video tutorial?

• Linear equations

• Transformations and cubic graphs

• Trigonometric functions

• Statistics and probability

Which transformation involves changing the size of a graph?

• Reflection

• Rotation

• Translation

• Dilation

What happens to a cubic graph when it is dilated by a factor of 2?

• It shifts upwards

• It reflects over the x-axis

• It becomes wider

• It becomes narrower

How does reflecting a cubic graph over the x-axis affect it?

• It remains unchanged

• It becomes wider

• It flips upside down

• It shifts to the right

What is the result of reflecting a quadratic graph over the y-axis?

• The graph shifts upwards

• The graph remains unchanged

• The graph becomes narrower

• The graph flips horizontally

What is the effect of translating a graph three units in a negative y-direction?

• The graph shifts upwards

• The graph becomes wider

• The graph shifts downwards

• The graph reflects over the x-axis

How do you transform the graph of y = x^3 to y = 2x + 3^3 - 4?

• By shifting to the left

• By rotating 90 degrees

• By dilating and translating

• By reflecting over the y-axis

What is the first step in transforming y = x^3 to y = 2x + 3^3 - 4?

• Reflect over the x-axis

• Translate by 4 units

• Dilate by a factor of 2

• Rotate 180 degrees

Which transformation does not change the shape of a graph?

• Translation

• Rotation

• Reflection

• Dilation

What is the effect of replacing y with y + 4 in a graph equation?

• The graph shifts downwards

• The graph shifts upwards

• The graph reflects over the y-axis

• The graph becomes narrower