Graphing Transformations and Dilations

The video tutorial guides students through the process of transforming a function graphically. It begins with setting up the problem and understanding the equation y = 2f(x) + 1. The teacher explains the concept of dilation, focusing on vertical stretching, and discusses translation and factorization. Students learn to apply these transformations to a graph, analyzing the changes in y-values while maintaining x-values. The tutorial concludes with graphing the final result and emphasizing the importance of precision in drawing graphs.

What is the first step before graphing the equation y = 2f(x) + 1?

• Rearrange the equation

• Change the function

• Start graphing immediately

• Ignore the equation

How does the number outside the brackets affect the graph?

• It changes the x-values

• It has no effect

• It causes a horizontal shift

• It affects the y-values through dilation

What type of transformation involves a slide or shift?

• Dilation

• Translation

• Rotation

• Reflection

What is the effect of a vertical dilation on the graph?

• It makes the graph wider

• It shifts the graph horizontally

• It rotates the graph

• It stretches or compresses the graph vertically

When applying transformations, which should be done first?

• Rotation

• Translation

• Reflection

• Dilation

What happens to the x-intercepts during a vertical dilation?

• They disappear

• They move down

• They remain unchanged

• They move up

How should you adjust the graph after applying a vertical dilation?

• Shift it left

• Shift it right

• Rotate it

• Move it up or down

Why is it recommended to use a pencil when graphing?

• To make it colorful

• To easily correct mistakes

• To make it permanent

• To draw faster

What is important about the vertex of a parabola?

• It should be at the origin

• It should be pointy

• It should be smooth

• It should be colored

What should you do if your graph is not precise?

• Leave it as is

• Start over

• Adjust and correct it

• Ignore it