Transformations of Linear Functions Explained

The video tutorial covers transformations of linear functions, starting with the definition of a family of functions and the parent function. It explains translations, including horizontal and vertical shifts, and provides examples. Reflections over the x-axis and y-axis are discussed, with examples of how to graph these transformations. The tutorial also covers horizontal and vertical stretches and shrinks, explaining how these transformations affect the graph of a function. The video concludes with a focus on understanding transformations rather than the original function.

What is the parent function for non-constant linear functions?

• f(x) = x^2

• f(x) = x

• f(x) = 2x + 1

• f(x) = 1/x

How is a horizontal translation of a function written?

• f(x) + k

• f(x - h)

• f(x) - k

• f(x + h)

If a function is shifted up by 3 units, how is it represented?

• f(x) + 3

• f(x - 3)

• f(x) - 3

• f(x + 3)

What type of transformation is represented by -f(x)?

• Reflection over the y-axis

• Vertical stretch

• Reflection over the x-axis

• Horizontal shrink

Which transformation flips the graph over the y-axis?

• f(-x)

• -f(x)

• f(x) + k

• f(x - h)

What happens to the graph of a function when it undergoes a horizontal stretch by a factor of 2?

• It becomes narrower

• It shifts up by 2 units

• It becomes wider

• It shifts right by 2 units

How is a vertical stretch by a factor of 3 represented?

• f(3x)

• 3f(x)

• f(x) + 3

• f(x) - 3

What does the transformation f(1/2x) represent?

• Vertical shrink by 2

• Horizontal shrink by 2

• Vertical stretch by 2

• Horizontal stretch by 2

If a function is transformed to f(x - 4), what type of transformation has occurred?

• Shift left by 4 units

• Shift right by 4 units

• Shift up by 4 units

• Shift down by 4 units

What does the transformation 1/3 f(x) represent?

• Vertical stretch by 3

• Horizontal shrink by 1/3

• Horizontal stretch by 3

• Vertical shrink by 1/3