Exploring Parent Functions and Transformations

This video tutorial covers the classification of functions into families based on common characteristics, focusing on parent functions. It explains how to identify function families using equations and graphs, and explores various transformations including translations, reflections, and dilations. The tutorial also demonstrates how to combine multiple transformations to alter the size, shape, position, and orientation of graphs.

What is the domain of a linear parent function?

• 0 to infinity

• 0 to 1

• -infinity to infinity

• 1 to infinity

What is the range of a quadratic function with its vertex at the origin?

• -infinity to infinity

• -infinity to 0

• 0 to infinity

• 1 to infinity

Which family does the function 'x^3' belong to?

• Quadratic

• Linear

• Square root

• Cubic

How do you identify a function's family from its equation?

• By its highest exponent

• By its graph shape

• By isolating x

• By removing operations

What does a vertical shift up do to a graph?

• Moves it left

• Moves it right

• Moves it down

• Moves it up

What does translating a function horizontally to the left involve?

• Adding to x inside the function

• Subtracting from x inside the function

• Adding to the function outside of x

• Subtracting from the function outside of x

What is the result of reflecting a function across the x-axis?

• It moves down

• It moves up

• It flips over the x-axis

• It flips over the y-axis

What indicates a reflection across the y-axis?

• Negative outside the function

• Positive outside the function

• Positive inside the function with x

• Negative inside the function with x

What does a dilation with a factor less than 1 do to a graph?

• Shrinks it horizontally

• Shrinks it vertically

• Stretches it vertically

• Stretches it horizontally

Combining transformations on a function can result in which of the following?

• Only horizontal shifts

• Only vertical shifts

• Any combination of transformations

• Only reflections