Graph Transformations and Functions

The video tutorial covers transformations of graphs, including stretches and translations, with a focus on applying these transformations to different functions such as linear, quadratic, and circular graphs. The tutorial provides step-by-step instructions on how to perform these transformations and explains the mathematical reasoning behind them. It also includes examples and practice questions to reinforce understanding.

What is the first step in transforming a graph when given a sequence of transformations?

• Rotate the graph

• Reflect the graph

• Stretch the graph

• Translate the graph

If a graph is stretched in the X direction by a factor of 0.5, what happens to the X coordinates?

• They are inverted

• They are halved

• They are doubled

• They remain the same

What is the effect of translating a graph upwards by 1 unit?

• The graph moves left

• The graph moves right

• The graph moves down

• The graph moves up

When transforming a circle, what does a translation of (7, -3) imply?

• Move 7 units down and 3 units right

• Move 7 units up and 3 units left

• Move 7 units right and 3 units down

• Move 7 units left and 3 units up

How do you determine the scale factor of a stretch in the Y direction for a circle?

• Divide the new diameter by the original diameter

• Add the original diameter to the new diameter

• Multiply the new diameter by the original diameter

• Subtract the original diameter from the new diameter

What is the result of applying a reflection in the Y-axis to a function?

• The function is inverted

• The function is shifted left

• The function is mirrored

• The function is stretched

In function notation, how is a stretch parallel to the X-axis with scale factor 2 represented?

• f(-2x)

• f(x/2)

• 2f(x)

• f(2x)

What transformation is needed to map a graph from (5, 3) to (5, 6)?

• Translation downwards

• Translation upwards

• Stretch in the Y direction

• Stretch in the X direction

How do you express a quadratic function in completing the square form?

• Factor out the leading coefficient

• Add and subtract the square of half the linear coefficient

• Divide the constant term by 2

• Multiply the quadratic term by 2