Understanding Linear Functions and Transformations

This video tutorial covers linear functions, focusing on transformations such as translations, reflections, and stretches. It explains how to manipulate the parent function f(x) = x by shifting, reflecting, and stretching it on a graph. The tutorial provides examples and notations for each transformation type, helping students understand how these changes affect the function's graph.

What is the most basic function in the family of linear functions?

• f(x) = x^2

• f(x) = 2x

• f(x) = x + 1

• f(x) = x

What is the parent function for linear functions?

• f(x) = 2x

• f(x) = x

• f(x) = x + 1

• f(x) = x^2

Which of the following is NOT a type of transformation?

• Exponentiation

• Rotation

• Reflection

• Translation

Which transformation involves shifting the graph of a function to a new position?

• Translation

• Reflection

• Shrink

• Stretch

How does a positive K value affect the vertical position of a function?

• Moves it left

• Moves it up

• Moves it right

• Moves it down

If a function is moved left by 3 units, what is the new function?

• f(x) = x - 3

• f(x) = x - 1

• f(x) = x + 3

• f(x) = x + 1

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

• The function shifts left

• The function shifts right

• The function flips vertically

• The function flips horizontally

What does a negative 'a' value do to a function?

• Shifts it left

• Shifts it right

• Flips it vertically

• Flips it horizontally

What happens to a function when it is horizontally stretched by a factor of 3?

• It becomes three times wider

• It becomes three times narrower

• It moves down by three units

• It moves up by three units

To vertically stretch a function, what must be true about the 'a' value?

• a = 0

• a > 1

• a < 0

• 0 < a < 1